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Global solutions to a new integrable equation with peakons. (English) Zbl 1062.35094

The Camassa-Holm shallow water wave equation is under consideration. Previously the integrability of this equation was obtained by constructing a Lax pair. The author proves the existence and uniqueness of global strong and weak solutions.

MSC:

35Q35 PDEs in connection with fluid mechanics
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35D05 Existence of generalized solutions of PDE (MSC2000)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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