Propagation of diverse solitary wave structures to the dynamical soliton model in mathematical physics

摘要

The extended sinh-Gordon equation expansion, the extended rational sine-cosine/sinh-cosh, and modified direct algebraic methods are employed to investigate the different solitary wave solutions to the (2+ l)-dimensional soliton model that plays a significant role in mathematical physics. The novel solutions are obtained in the different dark, bright, singular, and combined forms. Moreover, hyperbolic, trigonometric, rational, and singular periodic wave solutions are also recovered. Some solutions have been exemplified by graphical to understand the physical deportment of the proposed soliton model. The achieved outcomes are verified by putting them into the governing equation with the aid of Mathematica. The acquired results are valuable in grasping the elementary scenarios of nonlinear sciences as well as in the related nonlinear higher dimensional wave fields. The outcomes show that the governing model theoretically possesses extremely rich structures of solitary waves. Hence our techniques via fortification of symbolic computations provide an active and potent mathematical implement for solving diverse benevolent nonlinear wave problems.