Some exact invariant solutions and dynamical structures of multiple solitons for the (2+1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients using Lie symmetry analysis

The primary concern of the current work is dedicated to studying (2 + 1) dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients, which depicts the interaction of a Riemann wave proliferating along the y-axis and a long wave proliferating along the x-axis in a fluid. The extensive experience of getting innovative results via the method of Lie symmetry technique has been the core motivation of this research work. The considered equation has been reduced to lower dimensions and then finally to ordinary differential equations by employing the Lie symmetry technique. Subsequently, a variety of group invariant solutions is furnished with associated subalgebras. The dynamical analysis of acquired solutions with 3D plots leads to represent a rich diversity of solutions such as the periodic multi-solitons, single solitons, elasticinteraction between kink waves and lump-type multi-solitons and new solitary wave solutions, Wshaped solitons, and so on. Moreover, the obtained solutions, containing arbitrary functional parameters and other constant parameters, of the considered equation can be used to enrich the advanced behaviors of physical situations.