#### Vol. 4, No. 4, 2011

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Soliton dynamics for generalized $\mathrm{KdV}$ equations in a slowly varying medium

### Claudio Muñoz C.

Vol. 4 (2011), No. 4, 573–638
##### Abstract

We consider the problem of existence and global behavior of solitons for generalized Korteweg–de Vries equations (gKdV) with a slowly varying (in space) perturbation. We prove that such slowly varying media induce on the soliton dynamics large dispersive effects at large times. We also prove that, unlike the unperturbed case, there is no pure-soliton solution to the perturbed gKdV.

##### Keywords
generalized KdV equations, soliton dynamics, slowly varying medium
##### Mathematical Subject Classification 2000
Primary: 35Q51, 35Q53
Secondary: 37K10, 37K40