On the soliton dynamics under a slowly varying medium for generalized KdV equations

TL;DR

This paper investigates how slowly varying media influence soliton behavior in generalized KdV equations, revealing large dispersive effects and the absence of pure soliton solutions over time.

Contribution

It demonstrates the impact of inhomogeneities on soliton dynamics and proves the non-existence of pure-soliton solutions in slowly varying media regimes.

Findings

Large dispersive effects at large times due to inhomogeneities

No pure-soliton solutions exist in the studied regime

Inhomogeneities significantly alter soliton propagation

Abstract

We consider the problem of the soliton propagation, in a slowly varying medium, for a generalized Korteweg - de Vries equations (gKdV). We study the effects of inhomogeneities on the dynamics of a standard soliton. We prove that slowly varying media induce on the soliton solution large dispersive effects at large time. Moreover, unlike gKdV equations, we prove that there is no pure-soliton solution in this regime.