Variational derivation of two-component Camassa-Holm shallow water system

Details Variational derivation of two-component Camassa-Holm shallow water system Variational derivation of two-component Camassa-Holm shallow water system

2012-02-22

arxiv.org/abs/1202.5006v1

Physics

Mathematical Physics

to appear in Appl. Anal

Scientific paper

10.1080/00036811.2012.667082

By a variational approach in the Lagrangian formalism, we derive the nonlinear integrable two-component Camassa-Holm system (1). We show that the two-component Camassa-Holm system (1) with the plus sign arises as an approximation to the Euler equations of hydrodynamics for propagation of irrotational shallow water waves over a flat bed. The Lagrangian used in the variational derivation is not a metric.

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