Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation.
Cite
@article{arxiv.math-ph/0503016,
title = {Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves},
author = {S. I. Dejak and B. L. G. Jonsson},
journal= {arXiv preprint arXiv:math-ph/0503016},
year = {2007}
}
Comments
19 pages