Jacobi elliptic solutions, soliton solutions and other solutions to four higher-order nonlinear Schrodinger equations using two mathematical methods

Abstract

Two mathematical methods, via the (G′/G)-expansion method and extended auxiliary equation method are applied in this article to find many exact solutions with parameters of four higher-order nonlinear Schrodinger equations whose balance numbers are not positive integers, namely, the nonlinear Schrodinger equation with dual power-law nonlinearity, the higher-order dispersive nonlinear Schrodinger equation with both fourth-order dispersion effects and a quintic nonlinearity, the resonant nonlinear Schrodinger equation and the generalized higher-order nonlinear Schrodinger equation. When the parameters take up special values, the solitary and singular solitary wave solutions of these nonlinear Schrodinger equations are given. The used methods in this article present a wider applicability for handling nonlinear wave equations. Comparing our new results and the well-known results are obtained. Comparing the results resulting from the two methods with each others are also given.