He’s Semi-Inverse Method and Ansatz Approach to look for Topological and Non-Topological Solutions Generalized Nonlinear Schrödinger Equation

This paper obtains the exact 1-soliton solutions to generalized nonlinear Schrödinger equation. Nonlinear Schrödinger equation has been widely applied in many branches of nonlinear sciences such as nonlinear optics, nonlinear optical fibers and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theories and numerical studies. In this paper, the He’s semi-inverse method and the ansatz method are used to establish new exact solutions of generalized nonlinear Schrödinger equation. The results reveal that these methods are very effective and powerful tool for solving nonlinear fractional differential equations arising in mathematical physics.