Finding optical soliton solutions to nonlinear partial differential equations has become a popular topic in recent decades. The primary goal of this study is to identify a diverse collection of wave solutions to a generalized version of the nonlinear Schrödinger equation. We investigate two modifications to the generalized exponential rational function method to derive the expected results for this model. The first method is primarily based on using elementary functions such as exponential, trigonometric, and hyperbolic forms, which are commonly used to calculate the results. As for the second method, it is based on applying Jacobi elliptic functions to formulate solutions, whereas the underlying idea is the same as with the first method. As a means of enhancing the reader’s understanding of the results, we plot the graphical properties of our solutions. Based on this article’s results, it can be concluded that both techniques are easy to follow, and yet very efficient. These integration methods can determine different categories of solutions all in a unified framework. Therefore, it can be concluded from the manuscript that the approaches adopted in the manuscript may be regarded as efficient tools for determining wave solutions of a variety of partial differential equations. Due to the high computational complexity, the main requirement for applying our proposed methods is to employ an efficient computing software. Here, symbolic packages in Wolfram Mathematica have been used to validate the entire results of the paper.
