Optical solutions of the nonlinear conformable Schrödinger equation in weakly non-local media using two distinct analytic methods
摘要
This study investigates the cubic–quintic–septimal nonlinear Schrödinger equation with the conformable derivative, utilizing the extend Wang’s direct mapping method and the auxiliary equation approach. These techniques facilitate the derivation of various optical solutions, including dark, bright, mixed dark-bright, and wave soliton structures, within the framework of the nonlinear conformable Schrödinger model. The dynamic properties of these solutions are visualized through contour plots, as well as three-dimensional and two-dimensional graphical representations. The analysis underscores the significance of the cubic–quintic–septimal nonlinear Schrödinger wave equation, which plays a pivotal role in diverse areas such as optics, quantum mechanics, and nonlinear wave propagation studies. To the best of the authors’ knowledge, the findings of this research are all new and have not explored in other literature. Furthermore, the nonlinear conformable Schrödinger equation finds extensive applications in nonlinear optics, particularly in modeling the propagation of laser beams through media with nonlinear optical characteristics, highlighting the interaction and behavior of light in weakly non-local media.