Exact solution of the (2+1)-dimensional damping forcing coupled Burgers equation by using Darboux transformation

TL;DR

This paper derives exact solutions for a (2+1)-dimensional damping forcing coupled Burgers equation using Darboux transformation, revealing how damping and forcing influence wave behaviors.

Contribution

It establishes the Lax pair and constructs Darboux transformations for the equation, providing explicit wave solutions and analyzing effects of damping and forcing.

Findings

Derived N-fold Darboux transformation for the equation

Obtained solitary and periodic wave solutions

Graphically demonstrated damping and forcing effects

Abstract

In this article, we investigate the (2+1)-dimensional damping forcing coupled Burgers equation, which is obtain by adding damping and forcing terms from couple Burgers equation. The Lax pair of the (2+1)-dimensional damping forcing coupled Burgers equation is established. With the help of Lax pair, we derive the $N$-fold Darboux transformation of (2+1)-dimensional damping forcing coupled Burgers equation. Using one fold and two fold Darboux transformation, we demonstrated some wave solutions including solitary wave solution and periodic wave solution. The impact of damping and forcing terms in solitary wave solution and periodic solution is graphically demonstrated.