A dimensionally reduction approach to study kink soliton and its fission and fusion process of (3+1)-dimensional KdV-CDG equation

Abstract

The Hirota bilinear (HB) is a powerful and widely used technique to find various types of solitons of integrable systems. In this manuscript, we implement HB technique to find bilinear form of a dimensionally reduced (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation at z = x, z = y, and z = t. We present various results for distinct auxiliary function to study kink solitons and its fission and fusion dynamics. The MATLAB-2020 is used to display all the results via 3D and line 2D graphs for appropriate values of parameters. These findings provide a strong new insight into the nonlinear features of the model and lay the foundation for future studies in soliton dynamics and nonlinear events in related systems.