Nonlinear conformable Schrödinger equation in weakly nonlocal media using a new generalized computational technique
Muhammad Amin S. Murad, Mohammed A. Mustafa
Abstract
This study explores the cubic–quintic–septimal nonlinear conformable Schrödinger equation using a newly enhanced Kudryashov method. The refined approach yields various optical soliton solutions, including bright, dark, wave-type, M-shaped, and mixed dark–bright solitons, illustrating the method's versatility within the conformable derivative framework. The dynamics of these solutions are demonstrated using two-dimensional, three-dimensional, and contour plots. Additionally, modulation instability and sensitivity analysis are carried out to assess the stability and robustness of the model. The results highlight the significance of the conformable Schrödinger equation in modeling nonlinear wave propagation, particularly in weakly nonlocal media. The equation finds applications in nonlinear optics, quantum mechanics, and related fields, especially in describing laser beam propagation through media with nonlinear optical properties. The methodology presented in this work also shows potential for solving a broad class of nonlinear differential equations across multiple scientific disciplines.