An optimal system of Lie infinitesimals has been used in an investigation to find a solution to the (2+1)-dimensional Bogoyavlensky-Konopelchenko equation (BKE). This investigation was conducted to characterize certain fantastic characteristics of plasma-particle dispersion. A careful investigation into the Lie space with an unlimited number of dimensions was carried out to locate the relevant arbitrary functions. When developing accurate solutions for the BKE, it was necessary to establish an optimum system that could be employed in single, double, and triple combination forms.There were some fantastic wave solutions developed, and these were depicted visually. The Optimal Lie system demonstrates that it can obtain many accurate solutions to evolution equations.