Some novel analytical wave solutions to the nonlinear Schrödinger equation using two reliable methods

Abstract

In this article, some new traveling wave solutions to a (2+1)-dimensional version of the nonlinear Schrödinger equation are constructed through two analytical techniques. The main integration methods employed in this paper are the generalized exponential rational function method and the extended sinh–Gordon equation expansion method. These techniques enable us to integrate analytical solutions for the equation in many different structures. After finding solutions, a good description of the numerical behavior of obtained results in the form of several three-dimensional diagrams is also provided. One of the main advantages of employed methods is the relatively low cost and their straightforward structure compared to other existing techniques. Moreover, both methods determine analytical solutions of nonlinear models in terms of elementary functions. This distinctive feature enables us to employ them in solving other nonlinear problems as well. Necessary calculations in this article are done in symbolic form and within the framework of Maple software.