Analysis & PDE

  • Anal. PDE
  • Volume 4, Number 4 (2011), 573-638.

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

Claudio Muñoz

Full-text: Open access

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.

Article information

Source
Anal. PDE, Volume 4, Number 4 (2011), 573-638.

Dates
Received: 22 December 2009
Revised: 3 June 2010
Accepted: 13 July 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731169

Digital Object Identifier
doi:10.2140/apde.2011.4.573

Mathematical Reviews number (MathSciNet)
MR2872119

Zentralblatt MATH identifier
1264.35188

Subjects
Primary: 35Q51: Soliton-like equations [See also 37K40] 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 37K40: Soliton theory, asymptotic behavior of solutions

Keywords
generalized KdV equations soliton dynamics slowly varying medium

Citation

Muñoz, Claudio. Soliton dynamics for generalized $\mathrm{KdV}$ equations in a slowly varying medium. Anal. PDE 4 (2011), no. 4, 573--638. doi:10.2140/apde.2011.4.573. https://projecteuclid.org/euclid.apde/1513731169


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