Exact traveling wave solutions of the generalized fifth‐order dispersive equation by the improved Fan subequation method

Abstract

In this paper, the improved Fan subequation method is employed to construct exact traveling wave solutions for a generalized fifth‐order dispersive equation. By making use of bifurcation theory of dynamical systems, we have succeeded to obtain the phase portraits of the subequations involving all possible parameter conditions, and many different types of traveling wave solutions as well, which include more general soliton solutions, kink solutions, triangular function solutions, rational solutions, and Jacobian elliptic function solutions with double periods and so on. Furthermore, as all parameters in the representations of exact solutions are free variables, the solutions obtained show more complex dynamical behaviors and could be applicable to explain diversity in qualitative features of wave phenomena.