Exploring Soliton Behavior in Nonlinear Schrödinger Equation with Higher-Order Terms Via Extended Direct Algebraic Method

Abstract

We study the propagation of optical solitons in nonlinear media using a nonlinear Schrödinger equation with higher-order terms. We achieve accurate solutions as brilliant and dark solitons using the Extended Direct Algebraic Method (EDAM). The approach enables us to efficiently manage the dispersive and higher-order nonlinear factors. The impact of the coefficients on the soliton solutions is also investigated. Visual insights into the behaviour of the solitons are provided by the graphic analysis of the generated solutions using 2D and 3D plots. Furthermore, contour plots are created to show how the solutions vary depending on the different parameters, exposing complex structures and patterns. A greater comprehension of the physical phenomena that the equation describes is made possible by these graphical representations.