The generalized bifurcation method for deriving exact solutions of nonlinear space-time fractional partial differential equations

Abstract

In this paper, we develop a generalized bifurcation method to study exact solutions of nonlinear space-time fractional partial differential equations (PDEs), which is based on the bifurcation theory of dynamical systems. We present the procedure of the method and illustrate it with application to the space-time fractional Drinfel’d–Sokolov–Wilson equation. We identify all bifurcation conditions and derive the phase portraits of the system, from which we obtain different new exact solutions, and more interestingly, we find the so-called M/W-shaped solitary wave solutions. The results demonstrate the efficiency of the method in deriving exact solutions of space-time fractional PDEs.