Dynamical forms of various optical soliton solutions and other solitons for the new Schrödinger equation in optical fibers using two distinct efficient approaches

Abstract

In this work, the new nonlinear [Formula: see text]-dimensional Schrödinger (NLS) equation, which describes wave propagation in optical fibers, has been successfully studied using the [Formula: see text]-expansion method and the Unified method (UM). These techniques have been applied for the first time in extracting new analytic solutions for the mentioned NLS equation. The obtained solutions exhibit various types of optical solitons, including singular solitons, solitary waves, periodic solitons, and wave collisions. These solutions have wide-ranging applications in various fields such as fiber optics, telecommunication systems, plasma physics, hydrodynamics, and nonlinear optics. The behavior of the derived solutions has been visually represented using three-dimensional, two-dimensional, and contour plots, considering appropriate choices of the involved parameters within specific time intervals. These plots provide insights into the dynamics and characteristics of the solutions. The effectiveness, reliability, and ease of application of the [Formula: see text]-expansion method and the UM are demonstrated through the obtained solutions. These mathematical tools have proven to be powerful in solving nonlinear partial differential equations, offering valuable contributions to the field of mathematical physics, soliton theory and nonlinear sciences.