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Article Contents

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

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