Variational derivation of two-component Camassa-Holm shallow water system
arXiv:1202.5006 · doi:10.1080/00036811.2012.667082
Abstract
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.
to appear in Appl. Anal
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