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Periodic wave solutions and their limits for the generalized KP-BBM equation. (English) Zbl 1255.35183

Summary: We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B32 Bifurcations in context of PDEs
35B09 Positive solutions to PDEs
35B44 Blow-up in context of PDEs
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