The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation

E. S. Benilov, R. Grimshaw, E. P. Kuznetsova

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a fifth-order KdV equation, where the fifth-order derivative term is multiplied by a small parameter. It has been conjectured that this equation admits a non-local solitary wave solution which has a central core and an oscillatory tail either behind or in front of the core. We prove that this solution cannot be exactly steady, and instead the amplitude of the central core decays due to the energy flux generated in the oscillatory tail. The decay rate is calculated in the limit as the parameter tends to zero. In order to verify the analytical results, we have developed a high-precision spectral method for numerical integration of this equation. The analytical and numerical result show good agreement.

Original languageEnglish
Pages (from-to)270-278
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume69
Issue number3-4
DOIs
Publication statusPublished - 15 Dec 1993
Externally publishedYes

Fingerprint

Dive into the research topics of 'The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation'. Together they form a unique fingerprint.

Cite this