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

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

2007-11-29

arxiv.org/abs/0711.4701v1

Disc. Cont. Dyn. Syst.-A, 19 (2007), 531--543

Physics

Mathematical Physics

14 pages

Scientific paper

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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