Bifurcation Methods Of Dynamical Systems For Generalized Kadomtsov-petviashvili-benjamin-bona-mahony Equation

摘要

By applying the bifurcation theory of dynamical system to the generalized KP-BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves. 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 obtained.