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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

Delia Ionescu-Kruse 1,

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

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