Solitary Wave Solutions of Nonlinear Integro-Partial Differential Equations of 2 + 1 -Dimensional and Its Models

Abstract

The findings indicate an application of a new method of expansion of the forms $\left(Z^{\prime }/Z\right)$ and $\left(1/Z\right)$ to determine the solutions for wave of the solitary nature in the $\left(2+1\right)$ -dimensional modified form for nonlinear integro-partial differential equations. By using this strategy, we acquired solutions of wave which has a solitary nature that have been solved for three different kinds: hyperbolic, trigonometric, and rational functions. As a result, we obtained different forms of solutions which are new, effective, and powerful to illustrate the solitary nature of waves. The physical and geometrical interpretations have been shown using software in 2 and 3-dimensional surfaces. The obtained results have applications in mathematical and applied sciences. It can also solve different nonlinear integro-partial differential equations which have different applications in physical phenomena using this new method. It has many applications to solve the nonlinear nature of the physical world.