Application of the bifurcation method to the Whitham–Broer–Kaup-Like equations

In this paper, we investigate the Whitham–Broer–Kaup-Like equations. Some explicit expressions of solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.