Lie symmetry reductions and exact solutions of (2 + 1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation

The objective of this study is to investigate the generalized Calogero–Bogoyavlenskii–Schiff (gCBS) equation using Lie symmetry method. The gCBS equation characterizes the interaction between a Riemann wave moving in the y-axis and a long wave propagating along the x-axis. By applying the invariance principle of Lie group theory, the infinitesimal generators and corresponding Lie algebra are systematically derived. Utilizing the similarity function and variable, the symmetry reductions of gCBS equation is obtained, which result to an equivalent ordinary differential equation. Thus, a number of exact analytical solutions are constructed under specific parametric conditions. The physical behavior of these obtained solutions has been investigated using the numerical simulation. Accordingly, a variety of wave phenomena such as doubly soliton nature, parabolic, elastic multisoliton, multisoliton, and periodic wave profiles are illustrated through detailed graphical representation.