Solitons and other solutions to higher order nonlinear Schrödinger equation with non-Kerr terms using three mathematical methods

In this article, we apply three mathematical methods, via the (G′G)-expansion method, an auxiliary equation method and the sine-cosine method, to construct exact solutions with parameters for a higher-order nonlinear Schrödinger equations with non-Kerr terms. When the parameters take special values, the solitary wave solutions of this equation are derived. The used methods in this article present a wider applicability for handling nonlinear partial differential equations in mathematical physics. Comparison between the results yielding from the three methods is presented. Also, comparison between our new solutions of this Schrödinger equation and the well-known solutions is obtained.