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8,000 | Asymmetric Squares as Standing Waves in Rayleigh-Benard Convection | nlin.PS | Possibility of asymmetric square convection is investigated numerically using
a few mode Lorenz-like model for thermal convection in Boussinesq fluids
confined between two stress free and conducting flat boundaries. For relatively
large value of Rayleigh number, the stationary rolls become unstable and
asymmetric squar... | physics |
8,001 | Application of the Entropy Production Principle to the Analysis of the Morphological Stability of a Growing Cylindrical Crystal | nlin.PS | Stability of cylindrical and spherical crystals growing from a supersaturated
solution (in Mullins-Sekerka's approximation) is considered using the maximum
entropy production principle. The concept of the binodal of the nonequilibrium
(morphological) phase transition is introduced for interpretation of the
obtained res... | physics |
8,002 | Multi-component optical solitary waves | nlin.PS | We discuss several novel types of multi-component (temporal and spatial)
envelope solitary waves that appear in fiber and waveguide nonlinear optics. In
particular, we describe multi-channel solitary waves in bit-parallel-wavelength
fiber transmission systems for high performance computer networks, multi-colour
paramet... | physics |
8,003 | Period Stabilization in the Busse-Heikes Model of the Kuppers-Lortz Instability | nlin.PS | The Busse-Heikes dynamical model is described in terms of relaxational and
nonrelaxational dynamics. Within this dynamical picture a diverging alternating
period is calculated in a reduced dynamics given by a time-dependent
Hamiltonian with decreasing energy. A mean period is calculated which results
from noise stabili... | physics |
8,004 | Patterns and localized structures in bistable semiconductor resonators | nlin.PS | We report experiments on spatial switching dynamics and steady state
structures of passive nonlinear semiconductor resonators of large Fresnel
number. Extended patterns and switching front dynamics are observed and
investigated. Evidence of localization of structures is given. | physics |
8,005 | Spatial solitons in a semiconductor microresonator | nlin.PS | We show experimentally the existence of bright and dark spatial solitons in a
passive quantum-well-semiconductor resonator of large Fresnel number. For the
wavelength of observation the nonlinearity is mixed absorptive/defocusing.
Bright solitons appear more stable than dark ones. | physics |
8,006 | Raman solitons in transient SRS | nlin.PS | We report the observation of Raman solitons on numerical simulations of
transient stimulated Raman scattering (TSRS) with small group velocity
dispersion. The theory proceeds with the inverse scattering transform (IST) for
initial-boundary value problems and it is shown that the explicit theoretical
solution obtained b... | physics |
8,007 | Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection | nlin.PS | Patterns forming spontaneously in extended, three-dimensional, dissipative
systems are likely to excite several homogeneous soft modes ($\approx$
hydrodynamic modes) of the underlying physical system, much more than quasi
one- and two-dimensional patterns are. The reason is the lack of damping
boundaries. This paper co... | physics |
8,008 | Asymptotic Dynamics of Ripples | nlin.PS | A new nonlinear equation governing asymptotic dynamics of ripples is derived
by using a short wave perturbative expansion on a generalized version of the
Green-Naghdi system. It admits peakon solutions with amplitude, velocity and
width in interrelation and static compacton solutions with amplitude and width
in interre... | physics |
8,009 | Discreteness effects on soliton dynamics: a simple experiment | nlin.PS | We present a simple laboratory experiment to illustrate some aspects of the
soliton theory in discrete lattices with a system that models the dynamics of
dislocations in a crystal or the properties of adsorbed atomic layers. The
apparatus not only shows the role of the Peierls-Nabarro potential but also
illustrates the... | physics |
8,010 | Nonlinear Perturbation Theory | nlin.PS | An explicit perturbative solution to all orders is given for a general class
of nonlinear differential equations. This solution is written as a sum indexed
by rooted trees and uses the Green function of a linearization of the
equations. The modifications due to the presence of zero-modes is considered.
Possible diverge... | physics |
8,011 | Stability of Oscillating Hexagons in Rotating Convection | nlin.PS | Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation
in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons.
We study the stability of the oscillating hexagons using three coupled
Ginzburg-Landau equations. Close to the bifurcation point we derive reduced
equations for the ... | physics |
8,012 | Front motion for phase transitions in systems with memory | nlin.PS | We consider the Allen-Cahn equations with memory (a partial
integro-differential convolution equation). The prototype kernels are
exponentially decreasing functions of time and they reduce the
integrodifferential equation to a hyperbolic one, the damped Klein-Gordon
equation. By means of a formal asymptotic analysis we... | physics |
8,013 | Two-frequency forced Faraday waves: Weakly damped modes and pattern selection | nlin.PS | Recent experiments (Kudrolli, Pier and Gollub, 1998) on two-frequency
parametrically excited surface waves exhibit an intriguing "superlattice" wave
pattern near a codimension-two bifurcation point where both subharmonic and
harmonic waves onset simultaneously, but with different spatial wavenumbers.
The superlattice p... | physics |
8,014 | Incoherent optical switching of semiconductor resonator solitons | nlin.PS | We demonstrate experimentally the bistable nature of the bright spatial
solitons in a semiconductor microresonator and show that they can be created
and destroyed by incoherent local optical injection. | physics |
8,015 | Dynamics of Lattice Kinks | nlin.PS | In this paper we consider two models of soliton dynamics (the sine Gordon and
the \phi^4 equations) on a 1-dimensional lattice. We are interested in
particular in the behavior of their kink-like solutions inside the Peierls-
Nabarro barrier and its variation as a function of the discreteness parameter.
We find explicit... | physics |
8,016 | Experimental generation of steering odd dark beams of finite length | nlin.PS | In this work we report the first realization of odd dark beams of finite
length under controllable initial conditions. The mixed edge-screw phase
dislocations are obtained by reproducing binary computer-generated holograms.
Two effective ways to control the steering of the beams are analyzed
experimentally and compared... | physics |
8,017 | Spatial Solitons in Resonators | nlin.PS | We describe experiments testing the existence and investigating the
properties of spatial solitons in nonlinear resonators. We investigate the
properties of stationary and moving spatial solitons in lasers with saturable
absorber, with a subcritical bifurcation, as well as their manipulation. As
opposed, spatial solito... | physics |
8,018 | A Quasicrystallic Domain Wall in Nonlinear Dissipative Patterns | nlin.PS | We propose an indirect approach to the generation of a two-dimensional
quasiperiodic (QP) pattern in convection and similar nonlinear dissipative
systems where a direct generation of stable uniform QP planforms is not
possible. An {\it eightfold} QP pattern can be created as a broad transient
layer between two domains ... | physics |
8,019 | Four-phase patterns in forced oscillatory systems | nlin.PS | We investigate pattern formation in self-oscillating systems forced by an
external periodic perturbation. Experimental observations and numerical studies
of reaction-diffusion systems and an analysis of an amplitude equation are
presented. The oscillations in each of these systems entrain to rational
multiples of the p... | physics |
8,020 | Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems | nlin.PS | The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model
are studied using a phase dynamics approach. A Cross-Newell phase equation
describing slow and weak modulations of periodic stationary solutions is
derived. The derivation applies to the bistable, excitable, and the Turing
unstable regimes. In t... | physics |
8,021 | Nonlinear Stability of Bifurcating Front Solutions for the Taylor-Couette Problem | nlin.PS | We consider the Taylor-Couette problem in an infinitely extended cylindrical
domain. There exist modulated front solutions which describe the spreading of
the stable Taylor vortices into the region of the unstable Couette flow. These
transient solutions have the form of a front-like envelope advancing in the
laboratory... | physics |
8,022 | Non-linear Stability of Modulated Fronts for the Swift-Hohenberg Equation | nlin.PS | We consider front solutions of the Swift-Hohenberg equation $\partial_t u=
-(1+\partial_x^2)^2 u +\epsilon ^2 u -u^3$. These are traveling waves which
leave in their wake a periodic pattern in the laboratory frame. Using
renormalization techniques and a decomposition into Bloch waves, we show the
non-linear stability o... | physics |
8,023 | Spontaneous pattern formation in driven nonlinear lattice | nlin.PS | We demonstrate the spontaneous formation of spatial patterns in
a damped, ac-driven cubic Klein-Gordon
lattice. These
patterns are composed of arrays of intrinsic localized modes
characteristic for nonlinear lattices. We analyze the modulation
instability leading to this spontaneous pattern formation. Our
c... | physics |
8,024 | Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing | nlin.PS | We demonstrate that weak parametric interaction of a fundamental beam with
its third harmonic field in Kerr media gives rise to a rich variety of families
of non-fundamental (multi-humped) solitary waves. Making a comprehensive
comparison between bifurcation phenomena for these families in bulk media and
planar wavegui... | physics |
8,025 | Oscillations and defect turbulence in a shallow fluidized bed | nlin.PS | We report an experimental study of the dynamics of an air-fluidized thin
granular layer. Near-onset behavior of this shallow fluidized bed was described
in the earlier paper (Tsimring et al, 1999). Above the threshold of
fluidization the system exhibits a Hopf bifurcation as the layer starts to
oscillate at a certain f... | physics |
8,026 | Characterization of the Emergence of Order in an Oscillated Granular Layer | nlin.PS | The formation of textured patterns has been predicted to occur in two stages.
The first is an early time, domain-forming stage with dynamics characterized by
a disorder function $\bar\delta (\beta) \sim t^{-\sigma_{E}}$, with $\sigma_{E}
= {1/2}\beta$; this decay is universal. Coarsening of domains occurs in the
second... | physics |
8,027 | Parametric localized modes in quadratic nonlinear photonic structures | nlin.PS | We analyze two-color spatially localized modes formed by parametrically
coupled fundamental and second-harmonic fields excited at quadratic (or chi-2)
nonlinear interfaces embedded into a linear layered structure --- a
quasi-one-dimensional quadratic nonlinear photonic crystal. For a periodic
lattice of nonlinear inter... | physics |
8,028 | Breather initial profiles in networks of weakly coupled anharmonic oscillators | nlin.PS | Qualitative information about breather initial profiles in the weak coupling
limit of a chain of identical one-dimensional anharmonic oscillators is found
by studying the linearized equations of motion at a one-site breather. In
particular, information is found about how the breather initial profile depends
on its peri... | physics |
8,029 | Drifting Pattern Domains in a Reaction-Diffusion System with Nonlocal Coupling | nlin.PS | Drifting pattern domains (DPDs), moving localized patches of traveling waves
embedded in a stationary (Turing) pattern background and vice versa, are
observed in simulations of a reaction-diffusion model with nonlocal coupling.
Within this model, a region of bistability between Turing patterns and
traveling waves arise... | physics |
8,030 | Nonlocal Boundary Dynamics of Traveling Spots in a Reaction-Diffusion System | nlin.PS | The boundary integral method is extended to derive closed
integro-differential equations applicable to computation of the shape and
propagation speed of a steadily moving spot and to the analysis of dynamic
instabilities in the sharp boundary limit. Expansion of the boundary integral
near the locus of traveling instabi... | physics |
8,031 | Nearest pattern interaction and global pattern formation | nlin.PS | We studied the effect of nearest pattern interaction on a globally pattern
formation in a 2-dimensional space, where patterns are to grow initially from a
noise in the presence of periodic supply of energy. Although our approach is
general, we found that this study is relevant in particular to the pattern
formation on ... | physics |
8,032 | Multistep cascading and fourth-harmonic generation | nlin.PS | We apply the concept of multistep cascading to the problem of fourth-harmonic
generation in a single quadratic crystal. We analyze a new model of parametric
wave mixing and describe its stationary solutions for two- and three-color
plane waves and spatial solitons. Some applications to the optical frequency
division as... | physics |
8,033 | "Embedded solitons": solitary waves in resonance with the linear spectrum | nlin.PS | It is commonly held that a necessary condition for the existence of solitons
in nonlinear-wave systems is that the soliton's frequency (spatial or temporal)
must not fall into the continuous spectrum of radiation modes. However, this is
not always true. We present a new class of {\it % codimension-one} solitons
(i.e., ... | physics |
8,034 | Spatial period-multiplying instabilities of hexagonal Faraday waves | nlin.PS | A recent Faraday wave experiment with two-frequency forcing reports two types
of `superlattice' patterns that display periodic spatial structures having two
separate scales [1]. These patterns both arise as secondary states once the
primary hexagonal pattern becomes unstable. In one of these patterns (so-called
`superl... | physics |
8,035 | Pattern formation with a conservation law | nlin.PS | Pattern formation in systems with a conserved quantity is considered by
studying the appropriate amplitude equations. The conservation law leads to a
large-scale neutral mode that must be included in the asymptotic analysis for
pattern formation near onset. Near a stationary bifurcation, the usual
Ginzburg--Landau equa... | physics |
8,036 | Nonsteady condensation and evaporation waves | nlin.PS | We study motion of a phase transition front at a constant temperature between
stable and metastable states in fluids with the universal Van der Waals
equation of state (which is valid sufficiently close to the fluid's critical
point). We focus on a case of relatively large metastability and low viscosity,
when it can b... | physics |
8,037 | Solitons in nonlocal nonlinear media: exact results | nlin.PS | We investigate the propagation of one-dimensional bright and dark spatial
solitons in a nonlocal Kerr-like media, in which the nonlocality is of general
form. We find an exact analytical solution to the nonlinear propagation
equation in the case of weak nonlocality. We study the properties of these
solitons and show th... | physics |
8,038 | Ring dark solitary waves: experiment versus theory | nlin.PS | Theoretical and experimental results on optical ring dark solitary waves are
presented, emphasizing the interplay between initial dark beam contrast,
phase-shift magnitude, background-beam intensity and saturation of the
nonlinearity are presented. The results are found to confirm qualitatively the
existing analytical ... | physics |
8,039 | Scattering of light by molecules of light | nlin.PS | We study the scattering properties of optical dipole-mode vector solitons
recently predicted theoretically and generated in a laboratory. We demonstrate
that such a radially asymmetric composite self-trapped state resembles ``a
molecule of light'' which is extremely robust, survives a wide range of
collisions, and disp... | physics |
8,040 | Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors | nlin.PS | We predict the existence of spatiotemporal solitons (``light bullets'') in
two-dimensional self-induced transparency media embedded in a Bragg grating.
The "bullets" are found in an approximate analytical form, their stability
being confirmed by direct simulations. These findings suggest new possibilities
for signal tr... | physics |
8,041 | Directional coupling of optical signals by odd dark beams with mixed phase dislocations | nlin.PS | Numerical simulations on the evolution of step-screw and edge-screw optical
phase dislocations in bulk saturable self-defocusing nonlinear media are
presented, with emphasis on their ability to induce steering waveguides for
signal beams (pulses). Two schemes for directional coupling of such signals,
both ensuring reas... | physics |
8,042 | A simple model for the formation of vegetated dunes | nlin.PS | A simple model for the dynamics of dunes associated with vegetation is
proposed. Using the model, formation processes of transverse dunes, parabolic
dunes and elongated parabolic dunes according to two environmental factors:
i)the amount of sand at the source, ii)the wind force, are simulated. The
results have qualitat... | physics |
8,043 | Robustness of Quadratic Solitons with Periodic Gain | nlin.PS | We address the robustness of quadratic solitons with periodic
non-conservative perturbations. We find the evolution equations for
guiding-center solitons under conditions for second-harmonic generation in the
presence of periodic multi-band loss and gain. Under proper conditions, a
robust guiding-center soliton formati... | physics |
8,044 | Solitons in quadratic nonlinear photonic crystals | nlin.PS | We study solitons in one-dimensional quadratic nonlinear photonic crystals
with modulation of both the linear and nonlinear susceptibilities. We derive
averaged equations that include induced cubic nonlinearities and numerically
find previously unknown soliton families. The inclusion of the induced cubic
terms enables ... | physics |
8,045 | Stability of Spatial Optical Solitons | nlin.PS | We present a brief overview of the basic concepts of the soliton stability
theory and discuss some characteristic examples of the instability-induced
soliton dynamics, in application to spatial optical solitons described by the
NLS-type nonlinear models and their generalizations. In particular, we
demonstrate that the ... | physics |
8,046 | Observation of dipole-mode vector solitons | nlin.PS | We report on the first experimental observation of a novel type of optical
vector soliton, a {\em dipole-mode soliton}, recently predicted theoretically.
We show that these vector solitons can be generated in a photorefractive medium
employing two different processes: a phase imprinting, and a symmetry-breaking
instabi... | physics |
8,047 | On the boundary of the dispersion-managed soliton existence | nlin.PS | A breathing soliton-like structure in dispersion-managed (DM) optical fiber
system is studied. It is proven that for negative average dispersion the
breathing soliton is forbidden provided that a modulus of average dispersion
exceed a threshold which depends on the soliton amplitude. | physics |
8,048 | Dispersion-managed soliton in optical fibers with zero average dispersion | nlin.PS | The dispersion-managed (DM) optical system with step-wise periodical
variation of dispersion is studied in the framework of path-averaged
Gabitov-Turitsyn equation. The soliton solution is obtained by iterating the
path-averaged equation. The dependence of soliton parameters on dispersion map
strength is investigated t... | physics |
8,049 | Resonantly Forced Inhomogeneous Reaction-Diffusion Systems | nlin.PS | The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion
systems subject to periodic forcing with a spatially random forcing amplitude
field are investigated. Quenched disorder is studied using the resonantly
forced complex Ginzburg-Landau equation in the 3:1 resonance regime. Front
roughening and spon... | physics |
8,050 | Amplitude measurements of Faraday waves | nlin.PS | A light reflection technique is used to measure quantitatively the surface
elevation of Faraday waves. The performed measurements cover a wide parameter
range of driving frequencies and sample viscosities. In the capillary wave
regime the bifurcation diagrams exhibit a frequency independent scaling
proportional to the ... | physics |
8,051 | Derivation of Non-isotropic Phase Equations from a General Reaction-Diffusion Equation | nlin.PS | A non-isotropic version of phase equations such as the Burgers equation, the
K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney
equation in the three-dimensional space is systematically derived from a
general reaction-diffusion system by means of the renormalization group method. | physics |
8,052 | Nonlinearity and disorder: Classification and stability of nonlinear impurity modes | nlin.PS | We study the effects produced by competition of two physical mechanisms of
energy localization in inhomogeneous nonlinear systems. As an example, we
analyze spatially localized modes supported by a nonlinear impurity in the
generalized nonlinear Schr\"odinger equation and describe three types of
nonlinear impurity mode... | physics |
8,053 | Stable autosolitons in dispersive media with saturable gain and absorption | nlin.PS | We introduce the simplest one-dimensional model of a dispersive optical
medium with saturable dissipative nonlinearity and filtering (dispersive loss)
which gives rise to stable solitary pulses (autosolitons). In the particular
case when the dispersive loss is absent, the same model may also be interpreted
as describin... | physics |
8,054 | Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system | nlin.PS | A system consisting of the cubic complex Ginzburg-Landau equation which is
linearly coupled to an additional linear dissipative equation, is considered.
The model was introduced earlier in the context of dual-core nonlinear optical
fibers with one active and one passive cores. We argue that it may also
possibly describ... | physics |
8,055 | Bragg-grating solitons in a semilinear dual-core system | nlin.PS | We investigate the existence and stability of gap solitons in a double-core
optical fiber, where one core has the Kerr nonlinearity and the other one is
linear, with the Bragg grating (BG) written on the nonlinear core, while the
linear one may or may not have BG. The model considerably extends the
previously studied f... | physics |
8,056 | Multi-soliton energy transport in anharmonic lattices | nlin.PS | We demonstrate the existence of dynamically stable multihump solitary waves
in polaron-type models describing interaction of envelope and lattice
excitations. In comparison with the earlier theory of multihump optical
solitons [see Phys. Rev. Lett. {\bf 83}, 296 (1999)], our analysis reveals a
novel physical mechanism ... | physics |
8,057 | Destabilization and Localization of Traveling Waves by an Advected Field | nlin.PS | {We study a model of small-amplitude traveling waves arising in a
supercritical Hopf-bifurcation, that are coupled to a slowly varying, real
field. The field is advected by the waves and, in turn, affects their stability
via a coupling to the growth rate. In the absence of dispersion we identify two
distinct shortwave ... | physics |
8,058 | Travelling solitons in the parametrically driven nonlinear Schroedinger equation | nlin.PS | We show that the parametrically driven nonlinear Schroedinger equation has
wide classes of travelling soliton solutions, some of which are stable. For
small driving strengths nonpropogating and moving solitons co-exist while
strongly forced solitons can only be stably when moving sufficiently fast. | physics |
8,059 | Elliminating The Transverse Instabilities of Kerr Solitons | nlin.PS | We show analytically, numerically, and experimentally that a transversely
stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk
medium. The transverse instability of the soliton is completely eliminated if
it is made sufficiently incoherent along the transverse dimension. We derive a
criterion for ... | physics |
8,060 | Escape angles in bulk chi(2) soliton interactions | nlin.PS | We develop a theory for non-planar interaction between two identical type I
spatial solitons propagating at opposite, but arbitrary transverse angles in
quadratic nonlinear (or so-called chi(2)) bulk media. We predict quantitatively
the outwards escape angle, below which the solitons turn around and collide,
and above ... | physics |
8,061 | Quasiperiodic Patterns in Boundary-Modulated Excitable Waves | nlin.PS | We investigate the impact of the domain shape on wave propagation in
excitable media. Channelled domains with sinusoidal boundaries are considered.
Trains of fronts generated periodically at an extreme of the channel are found
to adopt a quasiperiodic spatial configuration stroboscopically frozen in time.
The phenomeno... | physics |
8,062 | Propagation and interaction of ultrashort electromagnetic pulses in nonlinear media with a quadratic-cubic nonlinearity | nlin.PS | Propagation of extremely short unipolar pulses of electromagnetic field
("videopulses") is considered in the framework of a model in which the material
medium is represented by anharmonic oscillators (approximating bound electrons)
with quadratic and cubic nonlinearities. Two families of exact analytical
solutions (wit... | physics |
8,063 | Light Bullet Modes in Self-Induced-Transparency Media with Refractive Index Modulation | nlin.PS | We predict the existence of a new type of spatiotemporal solitons ("light
bullets") in two-dimensional self-induced-transparency media with refractive
index modulation in the direction transverse to that of pulse propagation.
These self-localized guided modes are found in an approximate analytical form,
their existence... | physics |
8,064 | Spatiotemporal Patterns in Arrays of Coupled Nonlinear Oscillators | nlin.PS | Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal
patterns or structures. In this lecture, we point out that there is certain
advantage in studying discrete arrays, namely cellular neural/nonlinear
networks (CNNs), over continuous systems. Then, to illustrate these ideas, the
dynamics of diffu... | physics |
8,065 | Self-organized stable pacemakers near the onset of birhythmicity | nlin.PS | General amplitude equations for reaction-diffusion systems near to the soft
onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation
are derived. Using these equations and applying singular perturbation theory,
we show that stable autonomous pacemakers represent a generic kind of
spatiotemporal pa... | physics |
8,066 | A model for interacting instabilities and texture dynamics of patterns | nlin.PS | A simple model to study interacting instabilities and textures of resulting
patterns for thermal convection is presented. The model consisting of
twelve-mode dynamical system derived for periodic square lattice describes
convective patterns in the form of stripes and patchwork quilt. The interaction
between stationary ... | physics |
8,067 | Sideband Instabilities and Defects of Quasipatterns | nlin.PS | Quasipatterns have been found in dissipative systems ranging from Faraday
waves in vertically vibrated fluid layers to nonlinear optics. We describe the
dynamics of octagonal, decagonal and dodecagonal quasipatterns by means of
coupled Ginzburg-Landau equations and study their stability to sideband
perturbations analyt... | physics |
8,068 | Tunable front interaction and localization of periodically forced waves | nlin.PS | In systems that exhibit a bistability between nonlinear traveling waves and
the basic state, pairs of fronts connecting these two states can form localized
wave pulses whose stability depends on the interaction between the fronts. We
investigate the localization of waves within the framework of coupled
Ginzburg-Landau ... | physics |
8,069 | Propagation of Axi-Symmetric Nonlinear Shallow Water Waves over Slowly Varying Depth | nlin.PS | A problem in nonlinear water-wave propagation on the surface of an inviscid,
stationary fluid is presented.
The primary surface wave, suitably initiated at some radius, is taken to be a
slowly evolving nonlinear cylindrical wave (governed by an appropriate
Korteweg-de Vries equation); the depth is assumed to be varyi... | physics |
8,070 | Complexity at Mesoscale | nlin.PS | Through three examples we illustrate some of the concepts and ingredients
required for pattern formation at mesoscopic scales. Two examples build on
microscopic models where mesoscopic patterns emerge from homogeneous ground
states driven into instability by external forcing. In contrast, the third
example builds on a ... | physics |
8,071 | Model of the two level quantum dots ensemble interacting with coherent radiation | nlin.PS | We consider the model of quantum dots interacting with coherent radiation
when the relaxation processes may be neglected. The system under investigation
consists of two discrete energy levels of the quantum dots in the presence of
strong electron-electron Coulomb interaction and the transitions between these
levels in ... | physics |
8,072 | Propagation and interaction of extremely short electromagnetic pulses in non-linear media | nlin.PS | Propagation of the extremely short electromagnetic pulse in non-linear
dielectric media without the slowly varying envelope approximation is
discussed. The models under consideration take into account both resonant and
not-resonant excitations of non-linear medium, and polarisation states of
electromagnetic wave. Stead... | physics |
8,073 | Frequency Locking in Spatially Extended Systems | nlin.PS | A variant of the complex Ginzburg-Landau equation is used to investigate the
frequency locking phenomena in spatially extended systems. With appropriate
parameter values, a variety of frequency-locked patterns including flats, $\pi$
fronts, labyrinths and $2\pi/3$ fronts emerge. We show that in spatially
extended syste... | physics |
8,074 | Confinement and death of oscillations in coupled chaotic bistable oscillators | nlin.PS | In coupled chaotic bistable systems such as Lorenz and Chua oscillators,
two-phase domains corresponding to the two lobes of the strange attractor are
formed. The dynamics of each domain is confined to one lobe and typically
exhibits one of the two types of behavior: oscillation death or nearly periodic
oscillations. W... | physics |
8,075 | Square to stripe transition and superlattice patterns in vertically oscillated granular layers | nlin.PS | We investigated the physical mechanism for the pattern transition from square
lattice to stripes, which appears in vertically oscillating granular layers. We
present a continuum model to show that the transition depends on the
competition between inertial force and local saturation of transport. By
introducing multiple... | physics |
8,076 | Minimal speed of fronts of reaction-convection-diffusion equations | nlin.PS | We study the minimal speed of propagating fronts of convection reaction
diffusion equations of the form $u_t + \mu \phi(u) u_x = u_{xx} +f(u)$ for
positive reaction terms with $f'(0 >0$. The function $\phi(u)$ is continuous
and vanishes at $u=0$. A variational principle for the minimal speed of the
waves is constructed... | physics |
8,077 | Pattern Formation Near Onset of a Convecting Fluid In an Annulus | nlin.PS | Numerical simulations of the time-dependent Swift-Hohenberg equation are used
to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that
Rayleigh-Benard convection in the form of straight rolls or of an array of
dislocations may be observed in an annular domain depending on the values of
inner radius r_1, out... | physics |
8,078 | Accurate switching intensities and length scales in quasi-phase-matched materials | nlin.PS | We consider unseeded Type I second-harmonic generation in quasi-phase-matched
(QPM) quadratic nonlinear materials and derive an accurate analytical
expression for the evolution of the average intensity. The intensity-dependent
nonlinear phase mismatch due to the QPM induced cubic nonlinearity is found.
The equivalent f... | physics |
8,079 | Pattern and wavenumber selection in ferrofluids | nlin.PS | The formation of patterns of peaks on the free surface of a ferrofluid
subject to a magnetic field normal to the undisturbed interface is investigated
theoretically. The relative stability of ridge, square, and hexagon planforms
is studied using a perturbative energy minimization procedure. Extending
previous studies t... | physics |
8,080 | Resonance Effects in Topological Discrete sine-Gordon System | nlin.PS | We consider kink-antikink collisions in the topological discrete sine-Gordon
system. We find that the TDSG kink supports extra internal modes of vibration
and this results in resonance effects of the kind seen for the continuum phi^4
theory. | physics |
8,081 | Modulational instability in nonlocal nonlinear Kerr media | nlin.PS | We study modulational instability (MI) of plane waves in nonlocal nonlinear
Kerr media. For a focusing nonlinearity we show that, although the nonlocality
tends to suppress MI, it can never remove it completely, irrespectively of the
particular profile of the nonlocal response function. For a defocusing
nonlinearity th... | physics |
8,082 | One- and two-dimensional solitons in saturable media | nlin.PS | Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of
cubic-quintic and full saturable models are studied, starting from the full
system of the Maxwell's equations, rather than from the paraxial (NLS)
approximation. For the solitons with both TE and TM polarizations, it is shown
that there always exists ... | physics |
8,083 | Quadratic solitons in cubic crystals | nlin.PS | Starting from the Maxwell's equations and without resort to the paraxial
approximation, we derive equations describing stationary (1+1)-dimensional
beams propagating at an arbitrary direction in an optical crystal with cubic
symmetry and purely quadratic nonlinearity. The equations are derived
separately for beams with... | physics |
8,084 | Dispersion-managed soliton in a strong dispersion map limit | nlin.PS | A dispersion-managed optical system with step-wise periodical variation of
dispersion is studied in a strong dispersion map limit in the framework of
path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by
iterating the path-averaged equation analytically and numerically. An efficient
numerical alg... | physics |
8,085 | Stability of narrow beams in bulk Kerr-type nonlinear media | nlin.PS | We consider (2+1)-dimensional beams, whose transverse size may be comparable
to or smaller than the carrier wavelength, on the basis of an extended version
of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations.
As this equation is very cumbersome, we also study, in parallel to it, its
simplifie... | physics |
8,086 | Wavy stripes and squares in zero P number convection | nlin.PS | A simple model to explain numerically observed behaviour of chaotically
varying stripes and square patterns in zero Prandtl number convection in
Boussinesq fluid is presented. The nonlinear interaction of mutually
perpendicular sets of wavy rolls, via higher mode, may lead to a competition
between the two sets of wavy ... | physics |
8,087 | Zig-zag instability of an Ising wall in liquid crystals | nlin.PS | We present a theoretical explanation for the interfacial zigzag instability
that appears in anisotropic systems. Such an instability has been
experimentally highlighted for an Ising wall formed in a nematic liquid crystal
cell under homeotropic anchoring conditions. From an envelope equation,
relevant close to the Free... | physics |
8,088 | Drifting Abnormal Rolls in Electroconvection of Hybrid Aligned Nematic | nlin.PS | We report experimental and theoretical results on the conductive regime of
electroconvection in hybrid aligned nematics. The drifting oblique/normal rolls
below/above the Lifshitz frequency are observed at the onset of
electroconvection under a.c. voltage. The experimental data on the threshold
voltage, wavelength, obl... | physics |
8,089 | Crossover Between Flexoelectric Stripe Patterns and Electroconvection in Hybrid Aligned Nematics | nlin.PS | We report experimental and theoretical results on the flexoelectric
instability and crossover between flexoelectric domains and electroconvection
in a hybrid aligned nematic MBBA under d.c. voltage. At threshold a spatially
periodic flexoelectric deformation in the form of longitudinal domains (along
the planar directo... | physics |
8,090 | Observation of progressive motion of ac-driven solitons | nlin.PS | We report the first experimental observation of phase-locked motion of a
topological soliton at a nonzero average velocity in a periodically modulated
lossy medium, under the action of an ac force with no dc component [the effect
was predicted by G. Filatrella, B.A. Malomed, and R.D. Parmentier, Phys. Lett.
A 198, 43 (... | physics |
8,091 | Transition from oscillatory to excitable regime in a system forced at three times its natural frequency | nlin.PS | The effect of a temporal modulation at three times the critical frequency on
a Hopf bifurcation is studied in the framework of amplitude equations. We
consider a complex Ginzburg-Landau equation with an extra quadratic term,
resulting from the strong coupling between the external field and the unstable
modes. We show t... | physics |
8,092 | Statistical Theory for Incoherent Light Propagation in Nonlinear Media | nlin.PS | A novel statistical approach based on the Wigner transform is proposed for
the description of partially incoherent optical wave dynamics in nonlinear
media. An evolution equation for the Wigner transform is derived from a
nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that
random phase fluctuat... | physics |
8,093 | New connections between moving curves and soliton equations | nlin.PS | Lamb has identified a certain class of moving space curves with soliton
equations. We show that there are two other classes of curve evolution that may
be so identified. Hence three distinct classes of curve evolution are
associated with a given integrable equation. The nonlinear Schr\"{o}dinger
equation is used to ill... | physics |
8,094 | Semiconductor resonator solitons above band gap | nlin.PS | We show experimentally the existence of bright and dark spatial solitons in
semiconductor resonators for excitation above the band gap energy. These
solitons can be switched on, both spontaneously and with address pulses,
without the thermal delay found for solitons below the band gap which is
unfavorable for applicati... | physics |
8,095 | Spatial solitons in a pumped semiconductor resonator | nlin.PS | Bright and dark spatial solitons are observed in an optically pumped
semiconductor resonator. The pumping allows to considerably reduce the light
intensity necessary for the existence of the solitons and alleviates thermal
load problems. Experiments are found to agree with calculations based on a
simple large aperture ... | physics |
8,096 | Ramped-induced states in a parametrically driven Ginzburg-Landau equation | nlin.PS | We introduce a parametrically driven Ginzburg-Landau (GL) model, which admits
a gradient representation, and is subcritical in the absence of the parametric
drive (PD). In the case when PD acts uniformly in space, this model has a
stable kink solution. A nontrivial situation takes places when PD is itself
subject to a ... | physics |
8,097 | Families of Bragg-grating solitons in a cubic-quintic medium | nlin.PS | We investigate the existence and stability of solitons in an optical
waveguide equipped with a Bragg grating (BG) in which nonlinearity contains
both cubic and quintic terms. The model has straightforward realizations in
both temporal and spatial domains, the latter being most realistic. Two
different families of zero-... | physics |
8,098 | Generic features of modulational instability in nonlocal Kerr media | nlin.PS | The modulational instability (MI) of plane waves in nonlocal Kerr media is
studied for a general, localized, response function. It is shown that there
always exists a finite number of well-separated MI gain bands, with each of
them characterised by a unique maximal growth rate. This is a general property
and is demonst... | physics |
8,099 | Generalized Optimal Velocity Model for Traffic Flow | nlin.PS | A generalized optimal velocity model is analyzed, where the optimal velocity
function depends not only on the headway of each car but also the headway of
the immediately preceding one. The stability condition of the model is derived
by considering a small perturbation around the homogeneous flow solution. The
effect of... | physics |
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