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Bifurcations of traveling wave solutions for a generalized sinh-Gordon equation. (English) Zbl 1221.35367

Summary: We study the bifurcation behaviors and exact traveling wave solutions of the generalized sinh-Gordon equation under three different functions transformations by using the bifurcation theory of dynamical system. As a result, we obtained all possible traveling wave solutions such as solitary wave solutions, periodic wave solutions, breaking kink wave solutions and compactons under different parametric conditions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
35L70 Second-order nonlinear hyperbolic equations
35Q51 Soliton equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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