New soliton configurations for two different models related to the nonlinear Schrödinger equation through a graded-index waveguide

Abstract

The present paper studies two various models with two different types: the nonlinear Schrödinger equation with power-law nonlinearity and the (3 + 1)-dimensional nonlinear Schrödinger equation. We perform the modified (G′G)-expansion method to find some exact solutions and to construct various types of solitary wave phenomena for each equation. The received aspects contribute to the firm mathematical foundation and might be essential to the soliton waves. As a result, we obtain all the solutions from Wazwaz [Math. Comput. Modell. 43, 178–184 (2016)] and also obtain some new soliton solutions.