Authors:
Tozam Hossain,J. R. M. Borhan,Md. Mamun Miah,DOI NO:
https://doi.org/10.26782/jmcms.2025.07.00006Keywords:
The (3+1) - dimensional Geng equation,the exact travelling wave solutions,the (G^'/(G^'+G+A))-expansion strategy,the two variables (G'⁄G,1⁄G)-expansion strategy.,Abstract
We inspect a nonlinear partial differential equation, known as the Geng equation, which captures the behavior of systems such as shallow water wave dynamics and quantum field interactions and has notable applications in the areas of engineering sciences, mechanics, and quantum mechanics in the present research work. Multiple exact wave solutions are determined for the Geng equation by utilizing two effective strategies, namely, (G^'/(G^'+G+A))-expansion and two variables (G'⁄G,1⁄G)-expansion strategies. The solutions derived are formulated through elementary functions having rational, hyperbolic, exponential, and trigonometric forms. With specific values of chosen constants, the graphic representations of the obtained exact wave solutions are depicted using density, contour, 2D, and 3D plots to illuminate the inherent structure of the phenomenon. Additionally, we obtained kink-shaped, anti-kink-shaped, compacton, and singular-periodic-shaped solitons. The findings demonstrate that the mentioned strategies serve as influential mathematical tools and are shown to be highly efficient, computationally adaptable, and easily manageable for exploring solutions of nonlinear partial differential equations in mathematical physics.Refference:
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