Abstract
The dynamical behavior of a higher-order nonlinear Schrödinger equation is studied by using the bifurcation theory method of dynamical systems. With the aid of Maple, all bifurcations and phase portraits in the parametric space are obtained. Moreover, some new traveling wave solutions corresponding to the orbits on phase portraits are given, which include solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions.
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