A Review on Burgers' Equations and It's Applications - Kumar, Nand Kishor (Journal of Institute of Science and Technology, 2023)
This article presents a brief study on the review of the Burgers' equation. It also gives some concepts/ideas and techniques to solve Burgers' equation. Applying Burgers' equation to traffic flow requires concentrated effort for the solution. We develop our insights on how to obtain the Navier-Stokes equation through our inquiry into Burgers' equation. We also demonstrate how the Cole-Hopf transformation for the viscous Burgers' equation is derived. Finally, we use Burger's equation function as a model for the flow of traffic. Additionally, by employing the linear system method, we are able to obtain the answer to the one-way traffic flow problem. The Navier-Stokes equation has been derived to get in-viscid Burger's equation. The principle of Traffic flow and Navier-Stokes models have also been derived.