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Global conservative and multipeakon conservative solutions for the modified Camassa-Holm system with coupling effects. (English) Zbl 1407.35181
Summary: This paper investigates the continuation of solutions to the modified coupled two-component Camassa-Holm system after wave breaking. The underlying problem is rather challenging due to the mutual coupling effect between two components in the system. By introducing a novel transformation that makes use of a skillfully defined characteristic and a set of newly defined variables, the original system is converted into a Lagrangian equivalent system, from which the global conservative solution is obtained, which further allows for the establishment of the multipeakon conservative solution of the system. The results obtained herein are deemed useful for understanding the inevitable phenomenon near wave breaking.
MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35B60 Continuation and prolongation of solutions to PDEs
35M31 Initial value problems for mixed-type systems of PDEs
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