Unveiling new exact solutions of the unstable nonlinear Schrödinger equation using the improved modified Sardar sub-equation method

Abstract

The improved modified Sardar sub-equation method is used in this study to look into the complex domain of the unstable nonlinear Schrödinger equation, which is a basic idea in quantum physics. Our main goal is to obtain new and exact solutions for the unstable nonlinear Schrödinger equation, which includes various mathematical structures such as rational, exponential, trigonometric, and hyperbolic trigonometric forms. These solutions provide insight into the complex mechanics that control wave events and their nonlinear behavior. By employing MATLAB, we display visual depictions of these solutions in different dimensions, improving the direct examination of the occurrences. This study enhances the existing knowledge of mathematical methods for solving nonlinear differential equations, which can be applied to other nonlinear wave equations in other scientific fields. The findings from this work not only enhance our comprehension of the unstable nonlinear Schrödinger equation but also open up new possibilities for studying nonlinear phenomena in several physical systems, including optics, condensed matter physics, and quantum information science.