Open Access Research

Global conservative and multipeakon conservative solutions for the two-component Camassa-Holm system

Yujuan Wang and Yongduan Song*

Author Affiliations

School of Automation, Chongqing University, Chongqing, 400044, P.R. China

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Boundary Value Problems 2013, 2013:165  doi:10.1186/1687-2770-2013-165

Published: 10 July 2013

Abstract

The continuation of solutions for the two-component Camassa-Holm system after wave breaking is studied in this paper. The global conservative solution is derived first, from which a semigroup and a multipeakon conservative solution are established. In developing the solution, a system transformation based on a skillfully defined characteristic and a set of newly introduced variables is used. It is the transformation, together with the associated properties, that allows for the establishment of the results for continuity of the solution beyond collision time.

Keywords:
two-component Camassa-Holm system; Lagrangian system; global conservative solutions; conservative multipeakon solutions