On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations

Gianne Derks; Stephan van Gils

doi:10.1007/bf03167282

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On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations

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Peer reviewed

On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations

Gianne Derks and Stephan van Gils

Japan Journal of Industrial and Applied Mathematics, Vol.10(3), pp.413-430

10/1993

DOI: https://doi.org/10.1007/bf03167282

Abstract

bifurcation

traveling waves

elliptic integrals

KdV

We consider the perturbed Hamiltonian system uf = O~6H(u) - cP(u) with H(u) = v 1 2 lua)dx. We prove for vaxious perturbations P(u) that there is a f(2 ux + unique bifurcation point of traveling wave solutions on the curve of relative equilibria u~ such that H(u~) = m~n{H(u) I /u 2 = 9"}. As an additional result, the curve 9' ~ H(u-~) is proven to be concave.

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Title: On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations
Creators: Gianne Derks - University of Twente
Stephan van Gils
Publication Details: Japan Journal of Industrial and Applied Mathematics, Vol.10(3), pp.413-430
Publisher: Springer
Date published: 10/1993
Date accepted: 22/01/1993
Grant note: The research of G.D. was supported by the "Stichting voor Fundamenteil Onderzoek der Materie (FOM)" and the "Stichting Mathematisch Centrum (SMC)".
Identifiers: 99697160102346
Academic Unit: School of Maths and Physics
Resource Type: Journal article

On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations

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