Stability of solitary and cnoidal traveling wave solutions for a fifth order Korteweg-de Vries equation
Abstract
Stability analysis using Fourier transform positivity proves that soliton and cnoidal wave solutions of a fifth-order KdV equation are orbitally stable.
We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.
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