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

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September 2007, 19(3): 531-543. doi: 10.3934/dcds.2007.19.531

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

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

Received March 2007 Revised June 2007 Published July 2007

Abstract
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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.

Keywords: variational methods, flows with non-zero vorticity., Camassa-Holm equation, shallow water waves.

Mathematics Subject Classification: 35Q58, 76B15, 70G7.

Citation: Delia Ionescu-Kruse. Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 531-543. doi: 10.3934/dcds.2007.19.531

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