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Local well-posedness and blow-up criteria for a three-component Camassa-Holm type equation. (English) Zbl 1434.35165

Summary: Considered herein is a three-component Camassa-Holm type equation that admits a bi-Hamiltonian structure and infinitely many conserved quantities. In this paper, we establish the local well-posedness of this system in \(B_{p,r}^s\). We also deduce two blow-up criteria for this system.
©2020 American Institute of Physics

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35B44 Blow-up in context of PDEs
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
49K40 Sensitivity, stability, well-posedness
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