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New groups of solutions to the Whitham-Broer-Kaup equation. (English) Zbl 1457.35087

Summary: The Whitham-Broer-Kaup model is widely used to study the tsunami waves. The classical Whitham-Broer-Kaup equations are re-investigated in detail by the generalized projective Riccati-equation method. 20 sets of solutions are obtained of which, to the best of the authors’ knowledge, some have not been reported in literature. Bifurcation analysis of the planar dynamical systems is then used to show different phase portraits of the traveling wave solutions under various parametric conditions.

MSC:

35Q86 PDEs in connection with geophysics
86A15 Seismology (including tsunami modeling), earthquakes
35C07 Traveling wave solutions
35B32 Bifurcations in context of PDEs
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