Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system

Utilizing nonlinear evolution equations (NEEs) is common practice to establish the fundamental assumptions underlying natural phenomena. This paper examines the weakly dispersed non-linear waves in mathematical physics represented by the Konopelchenko-Dubrovsky (KD) equations. The \((G^\prime /G^2)\) $(G^{\prime }/G^2)$ -expansion method is used to analyze the model under consideration. Using symbolic computations, the \((G^\prime /G^2)\) $(G^{\prime }/G^2)$ -expansion method is used to produce solitary waves and soliton solutions to the \((2+1)\) $(2+1)$ -dimensional KD model in terms of trigonometric, hyperbolic, and rational functions. Mathematica simulations are displayed using two, three, and density plots to demonstrate the obtained solitary wave solutions’ behavior. These proposed solutions have not been documented in the existing literature.