New soliton solutions for a nonlinear complex hyperbolic Schrödinger dynamical equation with a truncated M-fractional derivative

Abstract

This research aims to derive novel soliton solutions for a complex hyperbolic Schr & ouml;dinger equation with a truncated M-fractional derivative. The selected equation is pivotal for its application in modeling various physical phenomena, such as nonlinear wave propagation in optical fibers and plasma physics, where conventional methods may fall short. We employed the modified generalized Kudryashov method and the modified exponential function method to obtain these solutions. These methods were chosen due to their effectiveness in solving nonlinear partial differential equations and their novelty in the context of this equation. The solutions obtained are stable solitons, localized wave packets that maintain their shape while propagating, and they are represented through trigonometric and hyperbolic functions. These solutions are significant for their potential applications in understanding and predicting wave behavior in optical and plasma systems. Additionally, we utilized software to analyze the wave functions, generating 3-D and 2-D contour plots based on specific parameters. These visualizations are essential for comprehending the solutions' physical configurations and dynamic processes in practical scenarios. The results confirm that the proposed methods are efficient for the analytic treatment of a wide variety of nonlinear partial differential equations with truncated M-fractional derivatives, enhancing our ability to model and analyze complex physical systems.