Soliton Dynamics of the Nonlinear Kodama Equation with M-Truncated Derivative via Two Innovative Schemes: The Generalized Arnous Method and the Kudryashov Method - Khizar Farooq; Ali. H. Tedjani; Zhao Li; Ejaz Hussain (Fractal and Fractional)
The primary aim of this research article is to investigate the soliton dynamics of the M-truncated derivative nonlinear Kodama equation, which is useful for optical solitons on nonlinear media, shallow water waves over complex media, nonlocal internal waves, and fractional viscoelastic wave propagation. We utilized two recently developed analytical techniques, the generalized Arnous method and the generalized Kudryashov method. First, the nonlinear Kodama equation is transformed into a nonlinear ordinary differential equation using the homogeneous balance principle and a traveling wave transformation. Next, various types of soliton solutions are constructed through the application of these effective methods. Finally, to visualize the behavior of the obtained solutions, three-dimensional, two-dimensional, and contour plots are generated using Maple (2023) mathematical software.