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Application of the bifurcation method to the Whitham-Broer-Kaup-like equations. (English) Zbl 1255.35182

Summary: We investigate the Whitham-Broer-Kaup-like equations. Some explicit expressions of solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B32 Bifurcations in context of PDEs
35B44 Blow-up in context of PDEs
35B10 Periodic solutions to PDEs
35C08 Soliton solutions
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