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On the Cauchy problem for the two-component Camassa-Holm system. (English) Zbl 1228.35092
The authors consider a two-component Camassa-Holm system, which includes the Camassa-Holm equation itself as a special case. This system is known to be integrable and to have a physical interpretation. They consider the question of existence and uniqueness for the initial value problem of this system. They also investigate whether or not this system admits wave-breaking phenomena similar to that of the Camassa-Holm equation itself. The authors claim to improve previously-known results for the system.
35G25Initial value problems for nonlinear higher-order PDE
35L15Second order hyperbolic equations, initial value problems
35B44Blow-up (PDE)
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