Qualitative Analysis and Explicit Exact Solitary, Kink and Anti-Kink Wave Solutions of the Generalized Nonlinear Schrodinger Equation with Parabolic Law Nonlinearity

摘要

The generalized nonlinear Schrodinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems. From a dynamic point of view, the existence of smooth solitary wave, kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, all possible explicit exact parametric representations of the waves are presented.