Bifurcations of travelling wave solutions for the generalized double sinh-Gordon equation

In this paper, 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.