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