Kinks and soliton solutions to the coupled Burgers equation by Lie symmetry approach

Abstract

The current research employs a novel class of invariant solutions to Painlevé integrable coupled Burgers equations. Many mathematical physics domains such as fluid dynamics, traffic flow, nonlinear acoustics, turbulence phenomena, and the interaction of convection and diffusion processes, use this fundamental model. The presented investigations utilize the Lie point symmetry to yield a class of exact solutions unknown in previous findings. Lie point symmetry reduces the number of independent variables in coupled Burgers equations. For the physical visualizations of the solutions, their profiles are analysed. Since arbitrary functions and constants are available in the solutions, the derived solutions have the potential to reveal rich physical structures. We next go over kink waves, multisoliton, line multisoliton and annihilation profiles in detail. We compute conserved vectors to demonstrate the integrability of CBEs. The results demonstrate their novelty, as they diverge completely from previous findings.