Symmetry analysis, optimal classification and dynamical structure of exact soliton solutions of (2+1)-dimensional modified Bogoyavlenskii–Schiff equation

Abstract The present research framework looks over complete sorted symmetry group classification and optimal subalgebras of (2+1)-dimensional modified Bogoyavlenskii-Schiff(mBSchiff) equation. It’s highly nonlinear and exhibits wave propagation in thermal pulse, sound wave, and bound particle. Using the invariance property of Lie groups, adequate infinitesimal symmetry of Lie algebra has been set up for the mBSchiff equation. A rigorous and systematized algorithm is carried out to obtain one optimal system based on the invariance feature of adjoint transformation. Further, symmetry reduction of the mBSchiff equation has been made to derive a system of ordinary differential equations with newly established similarity variables. The complete set of group invariant solutions for each corresponding subalgebras has been made. The derived solutions have diverse physical phenomena, which MATLAB simulation can quickly analyze. Thus, solutions presented here are kink, positon, soliton, doubly soliton, negaton, multisoliton types, which add on some meaningful physical aspects of the research.