Investigation of diverse genres exact soliton solutions to the nonlinear dynamical model via three mathematical methods

Abstract

This work aims to study new exact soliton solutions to the nonlinear Maccari’s system using the new extended direct algebraic method (NEDAM), the unified method, and the extended Sinh-Gordon equation expansion method (ShGEEM). Diverse genres exact soliton solutions are secured in the form of bright, dark, singular and in their combined behavior as bright-dark, dark-singular and periodic wave solutions. The Maccari system is a nonlinear model that represents the dynamics of waves, confined to a small part of space, in different regions such as nonlinear optics, plasma physics, mathematical physics, fluid mechanics, and hydrodynamics, etc. The secured solutions contain vital applications in engineering and physics. These solutions define the wave performance of the governance models. All the obtained solutions verified the considered model in this study. By choosing different parametric values, we established 3D, 2D and contour profiles for some selected solutions to describe the dynamic physical behavior of the acquired solutions. The novelty of the obtained results is discussed with a detailed comparison with the already existing results. The proposed methods are powerful and can be applied alternatively to recover new soliton solutions of different types of partial differential equations.