SOLITARY WAVE EFFECTS OF WOODS-SAXON POTENTIAL IN SCHRODINGER EQUATION WITH 3D CUBIC NONLINEARITY

Abstract

In this research article, we apply the generalized projective Riccati equation method to construct traveling wave solutions of the 3 d cubic focusing nonlinear Schrodinger equation with Woods-Saxon potential. The generalized projective Riccati equation method is a powerful and effective mathematical tool for obtaining exact solutions of nonlinear partial differential equations, and it allows us to derive a variety of traveling wave solutions of the 3d cubic focusing nonlinear Schrodinger equation with Woods-Saxon potential. These solutions contain periodic wave solutions, bright and dark soliton solutions. The study of many physical systems, such as Bose-Einstein condensates and nonlinear optics, that give rise to the nonlinear Schrodinger equation. We provide a detailed description of the generalized projective Riccati equation method in the paper, and demonstrate its usefulness in solving the nonlinear Schrodinger equation with Woods-Saxon potential. We present various graphical representations of the obtained solutions using MATLAB software, and analyze their characteristics. Our results provide new insights into the behavior of the 3 d cubic focusing nonlinear Schrodinger equation with Woods-Saxon potential, and have potential applications in numerous fields of physics, as well as nonlinear optics and condensed matter physics.