The extended Fan’s sub-equation method and its application to nonlinear Schrödinger equation with saturable nonlinearity

Abstract

This article discusses the saturable nonlinear Schrödinger equation, which is a key equation in the study of condensed matter physics, plasma physics, and nonlinear optics. This equation, which represents how electromagnetic waves behave in nonlinear media, is distinct because of its nonlinearity and dispersive properties. In this article, the extended Fan’s sub equation method is used to construct novel solitary wave solutions of the saturable nonlinear Schrödinger equation. This method is a powerful tool for dealing with nonlinear partial differential equations and has been used to a wide range of problems in several branches of mathematics. According to the this method, the saturable nonlinear Schrödinger equation admits a wide range of exact solution families that rely on five parameters. These solutions include soliton-like solutions, which are localized waves that maintain their shape and speed over long distances, and triangular-type solutions, which have a triangular shape. The study also identifies single and combined non-degenerate Jacobi elliptic function-like solutions. These solutions are a particular class of periodic function that appears in several branches of physics, including electromagnetism, quantum mechanics, and fluid dynamics. The obtained solutions are graphically represented by 3D, contour, and 2D graphs using MATLAB. The results of this article present novel perspectives on the saturable nonlinear Schrödinger equation and its possible applications in a different fields. These findings have important implications for nonlinear optics, the development of new optical devices, nonlinear optics, and related fields.