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Asymptotic profiles of solutions to the two-component Camassa-Holm system. (English) Zbl 1223.35275

Summary: We discuss the two-component Camassa-Holm system which arises in shallow water theory. This paper is concerned with the asymptotic description of solutions in the following sense: the corresponding solution to initial data with algebraic decay at infinity will retain this property at infinity in its lifespan.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
35L30 Initial value problems for higher-order hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
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