On extracting novel optical solutions to a higher order nonlinear Schrödinger’s equation

In recent years, different analytical methods have been employed for solving differential equations, including ordinary and partial derivatives. This paper aims to utilize the modified generalized exponential rational function method to extract different categories of analytical solutions to the generalized Schrödinger’s equation. The equation is one of the most effective tools in plasma physics to describe the interaction of traveling waves. In this paper, we derive some analytical solutions with singular wave solitons with exponentially increasing and decreasing amplitudes, with gradually increasing and decreasing amplitudes, and with constant amplitudes. In order to examine the dynamic behavior of the obtained solutions, some diagrams have been added to the article. It can be easily deduced that the employed technique provides a relatively simple and efficient way of determining analytical solutions. It should be noted that to the best of the author’s knowledge these techniques have not been utilized for solving in recent literature. Further, it can be easily adapted to handle other important nonlinear partial differential equations. All calculations can be carried out with the aid of computational software like Mathematica.