Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity

Delia Ionescu-Kruse

doi:10.3934/dcds.2007.19.531

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2007, Volume 19, Issue 3: 531-543. Doi: 10.3934/dcds.2007.19.531

This issue Previous Article On unique continuation for the modified Euler-Poisson equations Next Article Conformal and Geometric Properties of the Camassa-Holm Hierarchy

Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity

Delia Ionescu-Kruse^1,

1.
Institute of Mathematics Simion Stoilow of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest

Received: February 28, 2007

Revised: May 31, 2007

Published: August 2007

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Abstract

We describe the physical hypotheses underlying the derivation of an approximate model of water waves. For unidirectional surface shallow water waves moving over an irrotational flow as well as over a non-zero vorticity flow, we derive the Camassa-Holm equation by an interplay of variational methods and small-parameter expansions.

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Mathematics Subject Classification: 35Q58, 76B15, 70G75.

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Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity

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