Bifurcation analysis and exact solutions for a class of generalized time-space fractional nonlinear Schrödinger equations.

Abstract

In this work, we focus on a class of generalized time-space fractional nonlinear Schrödinger equations arising in mathematical physics. After utilizing the general mapping deformation method and theory of planar dynamical systems with the aid of symbolic computation, abundant new exact complex doubly periodic solutions, solitary wave solutions and rational function solutions are obtained. Some of them are found for the first time and can be degenerated to trigonometric function solutions. Furthermore, by applying the bifurcation theory method, the periodic wave solutions and traveling wave solutions with the corresponding phase orbits are easily obtained. Moreover, some numerical simulations of these solutions are portrayed, showing the novelty and visibility of the dynamical structure and propagation behavior of this model.