Exact breather waves solutions in a spatial symmetric nonlinear dispersive wave model in (2+1)-dimensions

In this article, the spatial symmetric nonlinear dispersive wave model in (2+1)-dimensions is studied, which have many applications in wave phenomena and soliton interactions in a two-dimensional space with time. In this framework, the Hirota bilinear form is applied to acquire diverse types of breather wave solutions from the foresaid equation. Abundant breather wave solutions are presented by the Hirota bilinear form and a mixture of exponentials and trigonometric functions with the usage of symbolic computation. In addition, the symbolic computation and the applied method for governing model are investigated. The movement role of the waves is investigated and the theoretical analysis of the acquired solutions is discussed using the bilinear technique of all produced solutions with 2D, density and 3D plots with respective parameters. The computational difficulties and outcomes highlight the clarity, effectiveness, and simplicity of the approaches, suggesting that these schemes can be applied to a variety of dynamic and static nonlinear equations governing evolutionary phenomena in computational physics as well as to other real-world situations and a wide range of academic fields.