Revisiting (2+1)-dimensional Burgers' dynamical equations: analytical approach and Reynolds number examination

Classical Burgers' equation is an indispensable dynamical evolution equation that is autonomously devised by Burgers and Harry Bateman in 1915 and 1948, respectively. This important model is featured through a nonlinear partial differential equation (NPDE). Furthermore, the model plays a crucial role in many areas of mathematical physics, including, for instance, fluid dynamics, traffic flow, nonlinear acoustics, turbulence phenomena, and linking convection and diffusion processes to state a few. Thus, in the present study, an efficient analytical approach by the name 'generalized Riccati equation approach' is adopted to securitize the class of (2+1)-dimensional Burgers' equations by revealing yet another set of analytical structures to the governing single and vector-coupled Burgers' equations. In fact, the besieged method of the solution has been proven to divulge various sets of hyperbolic, periodic, and other forms of exact solutions. Moreover, the method first begins by transforming the targeted NPDE to a nonlinear ordinary differential equation (NODE), and subsequently to a set of an algebraic system of equations; where the algebraic system is then solved simultaneously to obtain the solution possibilities. Lastly, certain graphical illustrations in 2- and 3-dimensional plots are set to be depicted - featuring the evolutional nature of the resulting structures, and thereafter, analyze the influence of the Reynolds number Ra on the respective wave profiles.