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Global conservative and multipeakon conservative solutions for the two-component Camassa-Holm system. (English) Zbl 1295.35148
Summary: 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.

MSC:
35B60 Continuation and prolongation of solutions to PDEs
35C08 Soliton solutions
35C07 Traveling wave solutions
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