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

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.

Submitted. Corrected some typos, updated references

References in corpus (4)

• Solitary Wave Dynamics in an External Potential
• Fast soliton scattering by delta impurities
• Soliton splitting by external delta potentials
• Description of the inelastic collision of two solitary waves for the BBM equation

Cited by in corpus (3)

• Sharp inelastic character of slowly varying NLS solitons
• Effective dynamics of double solitons for perturbed mKdV
• On approximate controllability of generalized KdV solitons