HAMILTONIAN AND NON-HAMILTONIAN MODELS FOR WATER WAVES.

Peter J Olver

Research output: Chapter in Book/Report/Conference proceedingConference contribution

76 Scopus citations

Abstract

A general theory for determining Hamiltonian model equations from noncanonical perturbation expansions of Hamiltonian systems is applied to the Boussinesq expansion for long, small amplitude waves in shallow water, leading to the Korteweg-de-Vries equation. New Hamiltonian model equations, including a natural 'Hamiltonian version' of the KdV equation, are proposed. The method also provides a direct explanation of the complete integrability (soliton property) of the KdV equation. Depth dependence in both the Hamiltonian models and the second order standard perturbation models is discussed as a possible mechanism for wave breaking.

Original languageEnglish (US)
Title of host publicationLecture Notes in Physics
EditorsPhilippe G. Ciarlet, Maurice Roseau
PublisherSpringer- Verlag
Pages273-290
Number of pages18
Edition195
ISBN (Print)3540129162
StatePublished - Dec 1 1984

Publication series

NameLecture Notes in Physics
Number195
ISSN (Print)0075-8450

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