Optical solutions to conformable nonlinear Schrödinger equation with cubic–quintic–septimal in weakly non-local media by new Kudryashov approach

This paper analyzes the cubic–quintic–septimal nonlinear Schrödinger equation with conformable derivative utilizing the new Kudryashov approach. Through this algorithm, several exact solutions are constructed within the present nonlinear conformable Schrödinger model such as bell-shaped, singular, bright, dark, mixed dark–bright, and wave soliton solutions. The physical behavior of these solutions is depicted via contour, three-dimensional, and two-dimensional representations. Moreover, it is crucial to emphasize the importance of analyzing the cubic–quintic–septimal nonlinear Schrödinger wave equation, which finds utility across a spectrum of fields including optics, quantum mechanics, and the study of nonlinear wave propagation. Besides, the approach holds promise for investigating diverse sets of differential equations within multiple domains of applied sciences. The governing nonlinear conformable Schrödinger equation also has numerous applications in nonlinear optics, such as describing the propagation of laser beams through materials with nonlinear optical properties. The inclusion of these nonlinearities illustrates the interaction and behavior of light beams in weakly non-local media.