This study is the first to use the extended rational sinh-cosh method and the modified extended tanh-function method to
obtain specific, appropriate solutions to the (2+1)-dimensional integro-differential Konopelchenko-Dubrovsky evolution
equation through mathematical construction of traveling wave solutions. The above model was transformed into a
nonlinear ordinary differential equation of third order using a traveling wave transformation. The model being studied
has several complex hyperbolic trigonometric and rational functions that may be used to find soli-tary and periodic wave
solutions. In order to emphasize the physical consequences of some of the solutions stated earlier, appropriate arbitrary
parameters have been used to create two- and three-dimensional visualizations. The effect of evolution over time on the
solution's structures has been shown in two-dimensional graphs.