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

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

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• On an integrable two-component Camassa-Holm shallow water system
• Singular solutions of a modified two-component Camassa-Holm equation
• The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations