Bifurcations and Exact Stationary Optical Solitons for the Cubic–Quartic Form of Nonlinear Refractive Index Together with Nonlinear Chromatic Dispersion

For three cubic–quartic optical soliton models of nonlinear refractive index together with nonlinear chromatic dispersion, the corresponding differential systems of the amplitude component are planar dynamical systems with a singular straight line. In this paper, by using the techniques from dynamical systems developed by Li & Chen, 2007 to analyze the parameter conditions of systems and construct the corresponding phase portraits, the dynamical behavior of the amplitude component can be analyzed. Under different parameter conditions, exact explicit envelope solitary wave solutions, periodic wave solutions, periodic peakons as well as the peakon solution, can all be found.