Different Wave Structures to the (2 + 1)-Dimensional Generalized Bogoyavlensky–Konopelchenko Equation

The purpose of the present work is to confirm the existence of different wave structures for the (2 + 1)-dimensional generalized Bogoyavlensky–Konopelchenko (2D-gBK) equation describing nonlinear waves in applied sciences. In this respect, based on the Hirota’s bilinear form and various test schemes, a variety of exact solutions, including breather-wave, rational, double soliton, mixed-type, cross-kink, and interaction solutions to the 2D-gBK equation are formally extracted. The dynamical structures of a series of selected solutions are investigated by portraying several 3-dimensional and density plots.