Soliton solutions to time-fractional nonlinear Schrödinger equation with cubic-quintic-septimal in weakly nonlocal media

Abstract

This paper examines the cubic-quintic-septimal (C-Q-S) nonlinear Schrödinger equation with conformable derivative, applied to the development of light beams in a weak nonlocal medium. The generalized exponential rational function technique (GERFM) is applied to analyze the present conformable nonlinear Schrödinger equation. The proposed method may provide several exact solutions, such as bell-shaped, dark-bright, kink, and wave soliton solutions. These solutions exhibit certain physical characteristics, which are illustrated using three-dimensional and two-dimensional. Furthermore, the method introduced in this paper provides accurate techniques for analyzing the solitary wave solutions in different forms of Schrödinger models, contributing to the understanding of light behavior in complex optical systems. The conformable nonlinear Schrödinger equation is widely recognized for its significant applications in nonlinear optics, especially in describing the propagation of laser beams through materials with nonlinear optical characteristics. These nonlinearities are crucial for understanding the interactions and dynamics of light beams in weakly non-local media.