Solitary waves with damped oscillatory tails: an analysis of the fifth-order Korteweg-de Vries equation

R. Grimshaw, B. Malomed, E. Benilov

Research output: Contribution to journalArticlepeer-review

Abstract

We construct oscillatory solitary wave solutions of a fifth-order Korteweg-de Vries equation, where the oscillations decay at infinity. These waves arise as a bifurcation from the linear dispersion curve at that wavenumber where the linear phase speed and group velocity coincide. Our approach is a wave-packet analysis about this wavenumber which leads in the first instance to a higher-order nonlinear Schrödinger equation, from which we then obtain the steady solitary wave solution. We then describe a complementary normal-form analysis which leads to the same result. In addition we derive the nonlinear Schrödinger equation for all wavenumbers, and list all the various anomalous cases.

Original languageEnglish
Pages (from-to)473-485
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume77
Issue number4
DOIs
StatePublished - 15 Oct 1994

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