Bifurcations and Exact Solutions of Generalized Nonlinear Schrödinger Equation with Nonlinear Chromatic Dispersion and Quintuple Power Law of Refractive Index in Optical Fibers

In this paper, we consider dynamics and exact solutions for the generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power law of refractive index in optical fibers. By investigating the bifurcations of phase portraits of the corresponding stationary solution system of the PDE model, we reveal the dynamical behavior of stationary envelope solutions. For the level curves having zero energy, we derive possible explicit exact parametric representations of the envelope soliton solutions, periodic solutions, peakon, periodic peakon as well as compacton solutions under given parameter conditions.