Vol. 4, No. 4, 2011

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ISSN: 1948-206X (e-only)
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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
Milestones
Received: 22 December 2009
Revised: 3 June 2010
Accepted: 13 July 2010
Published: 9 January 2012
Authors
Claudio Muñoz C.
Departamento de Ingeniería Matemática DIM
Universidad de Chile
Blanco Encalada 2120, piso 5, Casilla 170-3
Correo 3, Santiago
Chile
Department of Mathematics
The University of Chicago
5734 S. University Avenue
Chicago, IL 60637
United States
http://math.uchicago.edu/~cmunoz