Formation of optical soliton wave profiles of nonlinear conformable Schrödinger equation in weakly non-local media: Kudryashov auxiliary equation method

In this paper, we present an analysis of the cubic-quintic-septimal nonlinear Schr & ouml;dinger equation, which governs the evolution of light beams in a weak nonlocal medium with a conformable derivative, using the Kudryashov auxiliary equation method. The integral algorithm studied in this paper yields several exact solutions, including bell-shaped, singular, bright, dark, mixed dark-bright, and wave soliton solutions. The physical characteristics of these solutions are illustrated using contour, three-dimensional, and two-dimensional visualizations. Further, it is essential to highlight the significance of examining the cubic-quintic-septimal nonlinear Schr & ouml;dinger wave equation, as it has applications in a variety of fields such as optics, quantum mechanics, and nonlinear wave propagation studies. The study comprehensively investigates the impact of temporal variables and conformable order derivatives on the new optical soliton solutions, providing valuable insights into the dynamics and characteristics of the cubic-quintic-septimal nonlinear conformable Schr & ouml;dinger model. It is claimed that the governing conformable equation has a wide range of applications in nonlinear optics, including modeling the propagation of laser beams through materials with nonlinear optical characteristics. These nonlinearities capture the interactions and behaviors of light beams within weakly non-local media.