Unnamed: 0 int64 0 41k | title stringlengths 4 274 | category stringlengths 5 18 | summary stringlengths 22 3.66k | theme stringclasses 8
values |
|---|---|---|---|---|
8,100 | r-Matrix for the restricted KdV Flows with the Neumann constraints | nlin.SI | Under the Neumann constraints, each equation of the KdV hierarchy is
decomposed into two finite dimensional systems, including the well-known
Neumann model. Like in the case of the Bargmann constraint, the explicit Lax
representations are deduced from the adjoint representation of the auxiliary
spectral problem. It is ... | physics |
8,101 | Bilinearization of coupled nonlinear Schrödinger type equations: integrabilty and solitons | nlin.SI | Considering the coupled envelope equations in nonlinear couplers, the
question of integrability is attempted. It is explicitly shown that Hirota's
bilinear method is one of the simple and alternative techniques to Painlev\'e
analysis to obtain the integrability conditions of the coupled nonlinear
Schr\"odinger (CNLS) t... | physics |
8,102 | Neumann and Bargmann systems associated with an extension of the coupled KdV hierarchy | nlin.SI | An eigenvalue problem with a reference function and the corresponding
hierarchy of nonlinear evolution equations are proposed. The bi-Hamiltonian
structure of the hierarchy is established by using the trace identity. The
isospectral problem is nonlinearized as to be finite-dimensional completely
integrable systems in L... | physics |
8,103 | Quest for universal integrable models | nlin.SI | In this paper we discuss a universal integrable model, given by a sum of two
Wess-Zumino-Witten-Novikov (WZWN) actions, corresponding to two different
orbits of the coadjoint action of a loop group on its dual, and the
Polyakov-Weigmann cocycle describing their interactions. This is an effective
action for free fermion... | physics |
8,104 | Fermionic representation for basic hypergeometric functions related to Schur polynomials | nlin.SI | We present the fermionic representation for the q-deformed hypergeometric
functions related to Schur polynomials considered by S.Milne \cite{Milne}. For
$q=1$ these functions are also known as hypergeometric functions of matrix
argument which are related to zonal spherical polynomials for $GL(N,C)/U(N)$
symmetric space... | physics |
8,105 | Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice | nlin.SI | We report for the first time exact solutions of a completely integrable
nonlinear lattice system for which the dynamical variables satisfy a q-deformed
Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a
q-deformed lattice for which in continuum limit the equations of motion become
the envelope Ma... | physics |
8,106 | A new method to introduce additional separated variables for high-order binary constrained flows | nlin.SI | Degrees of freedom for high-order binary constrained flows of soliton
equations admitting $2\times 2$ Lax matrices are $2N+k_0$. It is known that
$N+k_0$ pairs of canonical separated variables for their separation of
variables can be introduced directly via their Lax matrices. In present paper
we propose a new method t... | physics |
8,107 | (2+0)-Dimensional Integrable Equations and Exact Solutions | nlin.SI | We propose a nonlinear $\sigma$-model in a curved space as a general
integrable elliptic model. We construct its exact solutions and obtain energy
estimates near the critical point. We consider the Pohlmeyer transformation in
Euclidean space and investigate the gauge equivalence conditions for a broad
class of elliptic... | physics |
8,108 | n-Dimensional Bateman Equation and Painleve Analysis of Wave Equations | nlin.SI | In the Painleve analysis of nonintegrable partial differential equations one
obtains differential constraints describing the movable singularity manifold.
We show, for a class of n-dimensional wave equations, that these constraints
have a general structure which is related to the $n$-dimensional Bateman
equation. In pa... | physics |
8,109 | The Supercomplexifications And Odd Bihamiltonians Structures | nlin.SI | The general method of the cojmplex supersymmetrization
(supercomplexifications) of the soliton equations with the odd (bi)
hamiltoninan structure is established. New version of the supercomplexified
Kadomtsev-Petvishvili hierarchy is given. The second odd Hamiltonina operator
of the SUSY KdV equation generates the odd ... | physics |
8,110 | Poisson Algebras associated with Constrained Dispersionless Modified KP Hierarchies | nlin.SI | We investigate the bi-Hamiltonian structures associated with constrained
dispersionless modified KP hierarchies which are constructed from truncations
of the Lax operator of the dispersionless modified KP hierarchy. After
transforming their second Hamiltonian structures to those of Gelfand-Dickey
type, we obtain the Po... | physics |
8,111 | Integrable impurities for an open fermion chain | nlin.SI | Employing the graded versions of the Yang-Baxter equation and the reflection
equations, we construct two kinds of integrable impurities for a small-polaron
model with general open boundary conditions: (a) we shift the spectral
parameter of the local Lax operator at arbitrary sites in the bulk, and (b) we
embed the impu... | physics |
8,112 | Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schrödinger equation | nlin.SI | We consider in detail the self-trapping of a soliton from a wave pulse that
passes from a defocussing region into a focussing one in a spatially
inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger
equation in which the dispersion coefficient changes its sign from normal to
anomalous. The model has d... | physics |
8,113 | Super KP equations and Darboux transformations: another perspective on the Jacobian Super KP hierarchy | nlin.SI | We generalize to the supersymmetric case the representation of the KP
hierarchy as a set of conservation laws for the generating series of the
conserved densities. We show that the hierarchy so obtained is isomorphic to
the JSKP of Mulase and Rabin. We identify its ``bosonic content'' with the
so-called Darboux-KP hier... | physics |
8,114 | On the Drach superintegrable systems | nlin.SI | Cubic invariants for two-dimensional degenerate Hamiltonian systems are
considered by using variables of separation of the associated St\"ackel
problems with quadratic integrals of motion. For the superintegrable St\"ackel
systems the cubic invariant is shown to admit new algebro-geometric
representation that is far mo... | physics |
8,115 | Reductions of the Volterra and Toda chains | nlin.SI | The Volterra and Toda chains equations are considered. A class of special
reductions for these equations are derived. | physics |
8,116 | On the calculation of finite-gap solutions of the KdV equation | nlin.SI | A simple and general approach for calculating the elliptic finite-gap
solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is
based on the use of the finite-gap equations and the general representation of
these solutions in the form of rational functions of the elliptic Weierstrass
function. The ... | physics |
8,117 | On the structure of the Bäcklund transformations for the relativistic lattices | nlin.SI | The B\"acklund transformations for the relativistic lattices of the Toda type
and their discrete analogues can be obtained as the composition of two duality
transformations. The condition of invariance under this composition allows to
distinguish effectively the integrable cases. Iterations of the B\"acklund
transforma... | physics |
8,118 | Finite-genus solutions for the Hirota's bilinear difference equation | nlin.SI | The finite-genus solutions for the Hirota's bilinear difference equation are
constructed using the Fay's identities for the theta-functions of compact
Riemann surfaces. | physics |
8,119 | Bihamiltonian geometry and separation of variables for Toda lattices | nlin.SI | We discuss the bihamiltonian geometry of the Toda lattice (periodic and
open). Using some recent results on the separation of variables for
bihamiltonian manifolds, we show that these systems can be explicitly
integrated via the classical Hamilton-Jacobi method in the so-called
Darboux-Nijenhuis coordinates. | physics |
8,120 | The method of Poisson pairs in the theory of nonlinear PDEs | nlin.SI | The aim of these lectures is to show that the methods of classical
Hamiltonian mechanics can be profitably used to solve certain classes of
nonlinear partial differential equations. The prototype of these equations is
the well-known Korteweg-de Vries (KdV) equation. In these lectures we touch the
following subjects: i)... | physics |
8,121 | Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in ${\bf R}^3$ | nlin.SI | It is shown, that any sufficiently smooth periodic solution of the
self-focusing Nonlinear Schr\"odinger equation can be approximated by periodic
finite-gap ones with an arbitrary small error. As a corollary an analogous
result for the motion of closed curves in ${\Bbb R}^3$ guided by the Filament
equation is proved. T... | physics |
8,122 | Conformal covariance in 2d conformal and integrable models, in W-algebras and in their supersymmetric extensions | nlin.SI | Conformal symmetry underlies the mathematical description of various
two-dimensional integrable models (e.g. for their Lax representation, Poisson
algebra, zero curvature representation,...) or of conformal models (for the
anomalous Ward identities, operator product expansion, Krichever-Novikov
algebra,...) and of W-al... | physics |
8,123 | Dispersionless sTB | nlin.SI | We analyze the dispersionless limits of the SUSY TB-B (sTB-B) and the SUSY TB
(sTB) hierarchies. We present the Lax description for each of these models, as
well as the N=2 sTB hierarchy and bring out various properties associated with
them. We also discuss open questions that need to be addressed in connection
with th... | physics |
8,124 | Deriving N-soliton solutions via constrained flows | nlin.SI | The soliton equations can be factorized by two commuting x- and t-constrained
flows. We propose a method to derive N-soliton solutions of soliton equations
directly from the x- and t-constrained flows. | physics |
8,125 | Integrable Discretization of the Coupled Nonlinear Schrödinger Equations | nlin.SI | A discrete version of the inverse scattering method proposed by Ablowitz and
Ladik is generalized to study an integrable full-discretization (discrete time
and discrete space) of the coupled nonlinear Schr\"{o}dinger equations. The
generalization enables one to solve the initial-value problem. Soliton
solutions and con... | physics |
8,126 | On dbar-problem and integrable equations | nlin.SI | Using the dbar-problem and dual dbar-problem, we derive bilinear relations
which allows us to construct integrable hierarchies in different
parametrizations, their Darboux-B\"{a}cklund transformations and to analyze
constraints for them ina very simple way. Scalar KP, BKP and CKP hierarchies
are considered as examples. | physics |
8,127 | Integrability of the $D_n^2$ vertex models with open boundary | nlin.SI | We investigate various aspects of the integrability of the vertex models
associated to the $D_n^2$ affine Lie algebra with open boundaries. We first
study the solutions of the corresponding reflection equation compatible with
the minimal symmetry of this system. We find three classes of general
solutions, one diagonal ... | physics |
8,128 | On Baxter Q-operators for Toda Chain | nlin.SI | We suggest the procedure of the construction of Baxter Q-operators for Toda
chain . Apart from the one-paramitric family of Q-operators, considered in our
recent paper (hep-th/9908179) we also give the construction of two basic
Q-operators and the derivation of the functional relations for these operators.
Also we have... | physics |
8,129 | A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability | nlin.SI | We present a fairly new and comprehensive approach to the study of stationary
flows of the Korteweg-de Vries hierarchy. They are obtained by means of a
double restriction process from a dynamical system in an infinite number of
variables. This process naturally provides us with a Lax representation of the
flows, which ... | physics |
8,130 | Generalized operator Yang-Baxter equations, integrable ODEs and nonassociative algebras | nlin.SI | Reductions for systems of ODEs integrable via the standard factorization
method (the Adler-Kostant-Symes scheme) or the generalized factorization
method, developed by the authors earlier, are considered. Relationships between
such reductions, operator Yang-Baxter equations, and some kinds of
non-associative algebras ar... | physics |
8,131 | Bethe Ansatz solutions for Temperley-Lieb Quantum Spin Chains | nlin.SI | We solve the spectrum of quantum spin chains based on representations of the
Temperley-Lieb algebra associated with the quantum groups ${\cal U}%
_{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a
modified version of the coordinate Bethe Ansatz through a suitable choice of
the Bethe states whic... | physics |
8,132 | Degenerate Poisson pencils on curves: new separability theory | nlin.SI | A review of a new separability theory based on degenerated Poisson pencils
and the so-called separation curves is presented. This theory can be considered
as an alternative to the Sklyanin theory based on Lax representations and the
so-called spectral curves. | physics |
8,133 | The classical massive Thirring system revisited | nlin.SI | We provide a complete treatment of algebro-geometric solutions of the
classical massive Thirring system. In particular, we study Dubrovin-type
equations for auxiliary divisors, consider the corresponding algebro-geometric
initial value problem, and derive the theta function representations of
algebro-geometric solution... | physics |
8,134 | Ellipticity Conditions for the Lax Operator of the KP Equations | nlin.SI | The Lax pseudo-differential operator plays a key role in studying the general
set of KP equations, although it is normally treated in a formal way, without
worrying about a complete characterization of its mathematical properties. The
aim of the present paper is therefore to investigate the ellipticity condition.
For t... | physics |
8,135 | On some nondecaying potentials and related Jost solutions for the heat conduction equation | nlin.SI | Potentials of the heat conduction operator constructed by means of 2 binary
Backlund transformations are studied in detail. Corresponding Darboux
transformations of the Jost solutions are introduced. We show that these
solutions obey modified integral equations and present their analyticity
properties. | physics |
8,136 | Point Symmetries of Generalized Toda Field Theories | nlin.SI | A class of two-dimensional field theories with exponential interactions is
introduced. The interaction depends on two ``coupling'' matrices and is
sufficiently general to include all Toda field theories existing in the
literature. Lie point symmetries of these theories are found for an infinite,
semi-infinite and finit... | physics |
8,137 | Point Symmetries of Generalized Toda Field Theories II Applications of the Symmetries | nlin.SI | The Lie symmetries of a large class of generalized Toda field theories are
studied and used to perform symmetry reduction. Reductions lead to generalized
Toda lattices on one hand, to periodic systems on the other. Boundary
conditions are introduced to reduce theories on an infinite lattice to those on
semi-infinite, o... | physics |
8,138 | N-soliton train interactions and perturbed complex Toda chain in nonlinear optics. Adiabatic and non-adiabtic aspects | nlin.SI | Our previous results on the N-soliton interaction in the adiabatic
approximation have been extended. It is shown that the complex Toda chain (CTC)
model is an universal one in the sense that it describes the N-soliton train
interactions for all NLEE from the NLS hierarchy. We derive the perturbed CTC
system and show th... | physics |
8,139 | First integrals generated by pseudosymmetries in Nambu-Poisson mechanics | nlin.SI | Some types of first integrals for Hamiltonian Nambu-Poisson vector fields are
obtained by using the notions of pseudosymmetries. In this theory, the
homogeneous Hamiltonian vector fields play a special role and we point out this
fact. The differential system which describe the $SU(2)$-monopoles is given as
example. The... | physics |
8,140 | On billiard weak solutions of nonlinear PDE's and Toda flows | nlin.SI | A certain class of partial differential equations possesses singular
solutions having discontinuous first derivatives ("peakons"). The time
evolution of peaks of such solutions is governed by a finite dimensional
completely integrable system. Explicit solutions of this system are constructed
by using algebraic-geometri... | physics |
8,141 | Rigidity, Functional Equations and the Calogero-Moser Model | nlin.SI | Suppose we have a natural Hamiltonian $H$ of $n$ particles on the line,
centre of mass momentum $P$ and a further independent quantity $Q$, cubic in
the momenta. If these are each $S_{n}$ invariant and mutually Poisson commute
we have the Calogero-Moser system with potential $V={1/6}\sum\limits_{i\neq
j}\wp(q_{i}-q_{j}... | physics |
8,142 | Integrability of V. Adler's discretization of the Neumann system | nlin.SI | We prove the integrability of the discretization of the Neumann system
recently proposed by V. Adler. | physics |
8,143 | On the behaviour of solutions to discrete time Lotka-Volterra equation | nlin.SI | The time evolution of a class of completely integrable discrete
Lotka-Volterra s ystem is shown not unique but have two different ways chosen
randomly at every s tep of generation. This uncertainty is consistent with the
existence of constant s of motion and disappears in both continuous time and
ultra discrete limits. | physics |
8,144 | A note on the super Krichever map | nlin.SI | We consider the geometrical aspects of the Krichever map in the context of
Jacobian Super KP hierarchy. We use the representation of the hierarchy based
on the Faa` di bruno recursion relations, considered as the cocycle condition
for the natural double complex associated with the deformations of super
Krichever data. ... | physics |
8,145 | Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles | nlin.SI | The scaled distribution of the smallest eigenvalue in the Laguerre orthogonal
and symplectic ensembles is evaluated in terms of a Painlev\'e V transcendent.
This same Painlev\'e V transcendent is known from the work of Tracy and Widom,
where it has been shown to specify the scaled distribution of the smallest
eigenvalu... | physics |
8,146 | Reductions of N-wave interactions related to low-rank simple Lie algebras. I: Z_2- reductions | nlin.SI | The analysis and the classification of all reductions for the nonlinear
evolution equations solvable by the inverse scattering method is an interesting
and still open problem. We show how the second order reductions of the N-wave
interactions related to low-rank simple Lie algebras g can be embedded also in
the Weyl gr... | physics |
8,147 | Principal models on a solvable group with nonconstant metric | nlin.SI | Field equations for generalized principle models with nonconstant metric are
derived and ansatz for their Lax pairs is given. Equations that define the Lax
pairs are solved for the simplest solvable group. The solution is dependent on
one free variable that can serve as the spectral parameter. Painleve analysis
of the ... | physics |
8,148 | Derivation of R-matrix from local Hamiltonian density | nlin.SI | A computer algebra algoritm for solving the quantum Yang-Baxter equation is
presented. It is based on the Taylor expansion of R-matrix which is developed
up to the order \lambda^6. As an example the classification of 4x4 R-matrices
is given. | physics |
8,149 | Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices | nlin.SI | We introduce a family of compatible Poisson brackets on the space of rational
functions with denominator of a fixed degree and use it to derive a
multi-Hamiltonian structure for a family of integrable lattice equations that
includes both the standard and the relativistic Toda lattices. | physics |
8,150 | From the solution of the Tsarev system to the solution of the Whitham equations | nlin.SI | We study the Cauchy problem for the Whitham modulation equations for monotone
increasing smooth initial data. The Whitham equations are a collection of
one-dimensional quasi-linear hyperbolic systems. This collection of systems is
enumerated by the genus g=0,1,2,... of the corresponding hyperelliptic Riemann
surface. E... | physics |
8,151 | The symplectic and twistor geometry of the general isomonodromic deformation problem | nlin.SI | Hitchin's twistor treatment of Schlesinger's equations is extended to the
general isomonodromic deformation problem. It is shown that a generic linear
system of ordinary differential equations with gauge group SL(n,C) on a Riemann
surface X can be obtained by embedding X in a twistor space Z on which sl(n,C)
acts. When... | physics |
8,152 | Elliptic Solitons and Groebner Bases | nlin.SI | We consider the solution of spectral problems with elliptic coefficients in
the framework of the Hermite ansatz. We show that the search for exactly
solvable potentials and their spectral characteristics is reduced to a system
of polynomial equations solvable by the Gr\"obner bases method and others. New
integrable pot... | physics |
8,153 | Recursion Operators of Some Equations of Hydrodynamic Type | nlin.SI | We give a general method for constructing recursion operators for some
equations of hydrodynamic type, admitting a nonstandard Lax representation. We
give several examples for N=2 and N=3 containing the equations of shallow water
waves and its generalizations with their first two higher symmetries and their
recursion o... | physics |
8,154 | Backlund transformations for the sl(2) Gaudin magnet | nlin.SI | Elementary, one- and two-point, Backlund transformations are constructed for
the generic case of the sl(2) Gaudin magnet. The spectrality property is used
to construct these explicitly given, Poisson integrable maps which are
time-discretizations of the continuous flows with any Hamiltonian from the
spectral curve of t... | physics |
8,155 | Unified Approach to KdV Modulations | nlin.SI | We develop a unified approach to integrating the Whitham modulation
equations. Our approach is based on the formulation of the initial value
problem for the zero dispersion KdV as the steepest descent for the scalar
Riemann-Hilbert problem, developed by Deift, Venakides, and Zhou, 1997, and on
the method of generating ... | physics |
8,156 | Bicomplex formulation and Moyal deformation of (2+1)-dimensional Fordy-Kulish systems | nlin.SI | Using bicomplex formalism we construct generalizations of Fordy-Kulish
systems of matrix nonlinear Schroedinger equations on two-dimensional
space-time in two respects. Firstly, we obtain corresponding equations in three
space-time dimensions. Secondly, a Moyal deformation is applied to the
space-time coordinates and t... | physics |
8,157 | Nonlinear Superposition Formulas Based on Lie Group SO(n+1,n) | nlin.SI | Systems of nonlinear ordinary differential equations are constructed, for
which the general solution is algebraically expressed in terms of a finite
number of particular solutions. Expressions of that type are called the
nonlinear superposition formulas. These systems are connected with local Lie
groups tranformations ... | physics |
8,158 | Conservation laws for the nonlinear Schrodinger equation in Miwa variables | nlin.SI | A compact expression for the generating function of the constants of motion
for the nonlinear Schrodinger equation is derived using the functional
representation of the AKNS hierarchy. | physics |
8,159 | Multisoliton solutions and integrability aspects of coupled nonlinear Schrodinger equations | nlin.SI | Using Painleve singularity structure analysis, we show that coupled
higher-order nonlinear Schrodinger (CHNLS) equations admit Painleve property.
Using the results of Painleve analysis, we succeed in Hirota bilinearizing the
CHNLS equations, one soliton and two soliton solutions are explictly obtained.
Lax pairs are ex... | physics |
8,160 | The spin 1/2 Calogero-Gaudin System and its q-Deformation | nlin.SI | The spin 1/2 Calogero-Gaudin system and its q-deformation are exactly solved:
a complete set of commuting observables is diagonalized, and the corresponding
eigenvectors and eigenvalues are explicitly calculated. The method of solution
is purely algebraic and relies on the co-algebra simmetry of the model. | physics |
8,161 | Abelian solitons | nlin.SI | We describe a new algebraically completely integrable system, whose integral
manifolds are co-elliptic subvarieties of Jacobian varieties. This is a
multi-periodic extension of the Krichever-Treibich-Verdier system, which
consists of elliptic solitons. | physics |
8,162 | Stokes Multipliers, Spectral Determinants and T-Q relations | nlin.SI | Recently, a remarkable correspondence has been unveiled between a certain
class of ordinary linear differential equations (ODE) and integrable models. In
the first part of the report, we survey the results concerning the 2nd order
differential equations, the Schroedinger equation with a polynomial potential.
We will ob... | physics |
8,163 | Baecklund transformations and Baxter's Q-operator | nlin.SI | The course of 5 lectures given at the seminar "Integrable Systems: from
Classical to Quantum" (Universite de Montreal, Jul 26 -- Aug 6, 1999) contains
a detailed comment on the recently discovered (Gaudin-Pasquier, 1992)
connection between Baecklund transformations in the theory of classical
integrable systems on one h... | physics |
8,164 | On the Benney Hierarchy: free energy, string equation and quantization | nlin.SI | The bi-Hamiltonian structure of the Benney hierarchy is revisited. We show
that the compatibility condition of the Poisson brackets provides the genus
zero free energy of a topological field theory coupled to 2d gravity. We
calculate the correlation functions via the Landau-Ginzburg formulation and
derive the string eq... | physics |
8,165 | Relativistic Toda chain | nlin.SI | Investigated is the relativistic periodic Toda chain, to each site of which
the ultra-local Weyl algebra is associated. Weyl's $q$ we are considering here
is restricted to be inside the unit circle. Quantum Lax operators of the model
are intertwined by six vertex $R$-matrix. Both independent Baxter's
$Q$-operators are ... | physics |
8,166 | N-wave interactions related to simple Lie algebras. Z_2- reductions and soliton solutions | nlin.SI | The reductions of the integrable N-wave type equations solvable by the
inverse scattering method with the generalized Zakharov-Shabat systems L and
related to some simple Lie algebra g are analyzed. The Zakharov- Shabat
dressing method is extended to the case when g is an orthogonal algebra.
Several types of one solito... | physics |
8,167 | Reductions and real forms of Hamiltonian systems related to N-wave type equations | nlin.SI | Reductions of N-wave type equations related to simple Lie algebras and the
hierarchy of their Hamiltonian structures are studied. The reduction group G_R
is realized as a subgroup of the Weyl group of the corresponding algebra. Some
of the reduced equations are of physical interest. | physics |
8,168 | Dynamical models of adiabatic $N $-soliton interactions | nlin.SI | The adiabatic N-soliton train interactions for the scalar nonlinear
Schrodinger (NLS) equation and its perturbed versions are well studied. Here we
briefly outline how they can be generalized for the higher NLS-type equations
and for the multicomponent NLS equations. It is shown that in all these cases
the complex Toda... | physics |
8,169 | Stationary structures in two-dimensional continuous Heisenberg ferromagnetic spin system | nlin.SI | Stationary structures in a classical isotropic two-dimensional continuous
Heisenberg ferromagnetic spin system are studied in the framework of the
(2+1)-dimensional Landau-Lifshitz model. It is established that in the case of
\vec S (\vec r, t)= \vec S (\vec r - \vec v t) the Landau-Lifshitz equation is
closely related... | physics |
8,170 | Deformations of dispersionless KdV hierarchies | nlin.SI | The obstructions to the existence of a hierarchy of hydrodynamic conservation
laws are studied for a multicomponent dispersionless KdV system. It is shown
that if an underlying algebra is Jordan, then the lowest obstruction vanishes
and that all higher obstructions automatically vanish. Deformations of these
multicompo... | physics |
8,171 | Hamiltonian Structures of KdV-Type Hierarchies and Associated W-Algebras | nlin.SI | The $(n,m)^{\th}$ KdV hierarchy is a restriction of the KP hierarchy to a
submanifold of pseudo-differential operators in a radio form. Explicit formula
of the restricted Hamiltonian structure of KP is given which provides a new,
more constructive proof of the isomorphism between the associated
$W(n,m)$-algebra to $W_{... | physics |
8,172 | Painleve Analysis in Superspace | nlin.SI | A method for carrying out the Painleve test in superspace is proposed. The
method is then applied to the one-parameter N=1 supersymmetric extensions of
the KdV equation. | physics |
8,173 | On Construction of Recursion Operator and Algebra of Symmetries for Field and Lattice Systems | nlin.SI | In the paper, developing the idea of V. Sokolov et all. (J.Math.Phys. 40
(1999)6473 we construct recursion operators and hereditary algebra of
symmetries for many field and lattice systems. | physics |
8,174 | Chains of KP, Semi-infinite 1-Toda Lattice Hierarchy and Kontsevich Integral | nlin.SI | There are well-known constructions of integrable systems which are chains of
infinitely many copies of the equations of the KP hierarchy ``glued'' together
with some additional variables, e.g., the modified KP hierarchy. Another
interpretation of the latter, in terms of infinite matrices, is called the
1-Toda lattice h... | physics |
8,175 | Jordan manifolds and dispersionless KdV equations | nlin.SI | Multicomponent KdV-systems are defined in terms of a set of structure
constants and, as shown by Svinolupov, if these define a Jordan algebra the
corresponding equations may be said to be integrable, at least in the sense of
having higher-order symmetries, recursion operators and hierarchies of
conservation laws. In th... | physics |
8,176 | Darboux first integral conditions and integrability of the 3D Lotka-Volterra system | nlin.SI | We apply the Darboux theory of integrability to polynomial ODE's of dimension
3. Using this theory and computer algebra, we study the existence of first
integrals for the 3-dimensional Lotka-Volterra systems with polynomial
invariant algebraic solutions linear and quadratic and determine numerous cases
of integrability... | physics |
8,177 | Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy | nlin.SI | Trigonometric non-isospectral flows are defined for KP hierarchy. It is
demonstrated that symmetry constraints of KP hierarchy associated with these
flows give rise to trigonometric Calogero-Moser system. | physics |
8,178 | Nonclassical symmetries as special solutions of heir-equations | nlin.SI | In (Nucci M.C. 1994, Physica D 78 p.124), we have found that iterations of
the nonclassical symmetries method give rise to new nonlinear equations, which
inherit the Lie point symmetry algebra of the given equation. In the present
paper, we show that special solutions of the right-order heir-equation
correspond to clas... | physics |
8,179 | Solutions of the Yang-Mills-Higgs equations in 2+1 dimensional anti-de Sitter space-time | nlin.SI | The solutions of the Bogomolny equation in anti-de Sitter space-time are
obtained by using Darboux transformations with both constant spectral
parameters and variable "spectral parameters". These solutions give the
Yang-Mills-Higgs fields in anti-de Sitter space-time. Some examples in SU(2)
case are considered and qual... | physics |
8,180 | Symplectic Structures for the Cubic Schrodinger equation in the periodic and scattering case | nlin.SI | We develop a unified approach for construction of symplectic forms for 1D
integrable equations with the periodic and rapidly decaying initial data. As an
example we consider the cubic nonlinear Schr\"{o}dinger equation. | physics |
8,181 | R-matrix for asymmetrical XXZ spin chain in magnetic field | nlin.SI | The R-matrix for asymmetrical XXZ spin chain in magnetic field is presented.
It depends non-additively on two spectral parameters. | physics |
8,182 | A geometric approach to singularity confinement and algebraic entropy | nlin.SI | A geometric approach to the equation found by Hietarinta and Viallet, which
satisfies the singularity confinement criterion but exhibits chaotic behavior,
is presented. It is shown that this equation can be lifted to an automorphism
of a certain rational surface and can therefore be considered to be the action
of an ex... | physics |
8,183 | On the relation between multifield and multidimensional integrable equations | nlin.SI | The new examples are found of the constraints which link the 1+2-dimensional
and multifield integrable equations and lattices. The vector and matrix
generalizations of the Nonlinear Schr\"odinger equation and the Ablowitz-Ladik
lattice are considered among the other multifield models. It is demonstrated
that using of t... | physics |
8,184 | Noncommutative integrability and recursion operators | nlin.SI | Geometric structures underlying commutative and non commutative integrable
dynamics are analyzed. They lead to a new characterization of noncommutative
integrability in terms of spectral properties and of Nijenhuis torsion of an
invariant (1,1) tensor field. The construction of compatible symplectic
structures is also ... | physics |
8,185 | Integrable Yang-Mills-Higgs Equations in 3-Dimensional De Sitter Space-Time | nlin.SI | This paper describes an integrable Yang-Mills-Higgs system on
(2+1)-dimensional de Sitter space-time. It is the curved-space-time analogue of
the Bogomolnyi equations for monopoles on R^3. A number of solutions, of
various types, are constructed. | physics |
8,186 | A new C-integrable limit of SHG equations | nlin.SI | A new C-integrable limit of the second harmonic generation equations is
found. The corresponding general solution is given in an explicit form.
Connection of this problem with the modified Liouville equation is discussed. | physics |
8,187 | Time dependence and (non)commutativity of symmetries of evolution equations | nlin.SI | We present easily verifiable sufficient conditions of time-independence and
commutativity for local and nonlocal symmetries for a large class of
homogeneous (1+1)-dimensional evolution systems. In contrast with the majority
of known results, the verification of our conditions does not require the
existence of master sy... | physics |
8,188 | Semiclassical Soliton Ensembles for the Focusing Nonlinear Schroedinger Equation | nlin.SI | We present a new generalization of the steepest descent method introduced by
Deift and Zhou for matrix Riemann-Hilbert problems and use it to study the
semiclassical limit of the focusing nonlinear Schroedinger equation with real
analytic, even, bell-shaped initial data. We provide explicit strong locally
uniform asymp... | physics |
8,189 | On Psi-function for finite-gap potentials | nlin.SI | A way to derive an explicit formulae in terms of the potentials, if they are
finite-gap, for the solutions of spectral problems and corresponding algebraic
curves is presented. | physics |
8,190 | Lie symmetries of difference equations | nlin.SI | The discrete heat equation is worked out in order to illustrate the search of
symmetries of difference equations. It is paid an special attention to the Lie
structure of these symmetries, as well as to their dependence on the derivative
discretization. The case of q-symmetries for discrete equations in a q-lattice
is a... | physics |
8,191 | Some Examples of RS^2_3(3)-Transformations of Ranks 5 and 6 as the Higher Order Transformations for the Hypergeometric Function | nlin.SI | A combination of rational mappings and Schlesinger transformations for a
matrix form of the hypergeometric equation is used to construct higher order
transformations for the Gauss hypergeometric function. | physics |
8,192 | Darboux Transformation and Exact Solutions in the model of Cylindrically Symmetrical Chiral Field | nlin.SI | The application of the Darboux Transformation method to the integrable model
of Cylindrically Symmetrical Chiral field has been considered. The associated
linear system of matrix equations has been proposed and the properties of
symmetrie for its solutions has been obtained. The necessary form of Darboux
Transformation... | physics |
8,193 | The Inverse Scattering Transform for a Model of Colomb's plasma with the negative temperature | nlin.SI | The boundary problem for a two-dimensional elliptical equation -sinh-Gordon
has been investigated. The exact solutions have been found and identities of
traces have been proposed. The application of the problem to the model of the
Coulomb's plasma with the negative temperature has been considered. | physics |
8,194 | An integrable discretization of KdV at large times | nlin.SI | An "exact discretization" of the Schroedinger operator is considered and its
direct and inverse scattering problems are solved. It is shown that a
differential-difference nonlinear evolution equation depending on two arbitrary
constants can be solved by using this spectral transform and that for a special
choice of the... | physics |
8,195 | Relativistic Toda chain at root of unity | nlin.SI | We declare briefly several interesting features of the quantum relativistic
Toda chain at N-th root of unity. We consider the finite dimensional
representation of the Weyl algebra. The origin of the features mentioned is
that we consider simultaneously the quantum finite dimensional part and the
classical dynamics of N... | physics |
8,196 | Towards an Inverse Scattering theory for non decaying potentials of the heat equation | nlin.SI | The resolvent approach is applied to the spectral analysis of the heat
equation with non decaying potentials. The special case of potentials with
spectral data obtained by a rational similarity transformation of the spectral
data of a generic decaying potential is considered. It is shown that these
potentials describe ... | physics |
8,197 | Non-autonomous Svinolupov Jordan KdV Systems | nlin.SI | Non-autonomous Svinolupov-Jordan systems are considered. The integrability
criteria of such systems are associated with the existence of recursion
operators. A new non-autonomous KdV system is obtained and its recursion
operator is given for all $N$. The examples for N=2 and N=3 are studied in
detail. Some possible tra... | physics |
8,198 | The Calogero equation and Liouville type equations | nlin.SI | In this paper we present a two-component generalization of the C-integrable
Calogero equation (see [1]). This system is C-integrable as well, and moreover
we show that the Calogero equation and its two-component generalization are
solvable by a reciprocal transformation to ODE's. Simultaneously we obtain a
generalized ... | physics |
8,199 | A Determinant Formula for a Class of Rational Solutions of Painlevé V Equation | nlin.SI | We give an explicit determinant formula for a class of rational solutions of
the Painlev\'e V equation in terms of the universal characters. | physics |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.