Bifurcation of traveling wave solutions for the BBM-like B(2, 2) equation

摘要

In this paper, we employ the bifurcation method of dynamical systems to investigate the BBM-like B(2, 2) equation. The phase portrait bifurcation of the traveling wave system corresponding to the equation is given. Under different parametric conditions, various sufficient conditions to guarantee the existence of smooth and non-smooth traveling wave solutions are given. Through some special phase orbits, Some solitary wave solutions expressed by implicit functions, periodic cusp wave solution, compacton solution and peakon solution are obtained.