Bifurcations of travelling wave solutions for the generalized double sinh-Gordon equation. (English) Zbl 1124.35077

Tang, Shengqiang; Huang, Wentao

Appl. Math. Comput. 189, No. 2, 1774-1781 (2007).

Summary: The generalized double sinh-Gordon equation is studied. The existence of periodic wave, solitary wave, kink and anti-kink wave and unbounded wave solutions is proved, by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
37K50	Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems

Keywords:

solitary wave; kink; anti-kink; unbounded travelling wave solution; periodic travelling wave

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