Analysis of soliton solutions to the nonlinear conformable Schrödinger equation in weakly non-local media using two analytic algorithms

This study explores the use of the modified simplest equation approach and the Kudryashov approach to derive optical solutions for the cubic-quintic-septimal nonlinear Schrödinger model with conformable derivative. The new optical soliton solutions, including kink-type, mixed dark-bright, bright, and wave solitons, are represented through combinations of trigonometric and hyperbolic functions. The dynamical attitude of the current soliton solutions, considering the effects of the temporal parameter and conformable derivative, is analyzed through various two-dimensional and three-dimensional graphs. These methods provide a systematic and dependable approach for investigating nonlinear phenomena, advancing both the field of nonlinear science and its practical applications. It is crucial to highlight the importance of studying the cubic-quintic-septimal nonlinear Schrödinger wave equation which has application in various fields such as quantum mechanics, optics, and nonlinear wave propagation. Understanding of its solutions facilitates the design and optimization of systems involving weak non-local media.