Residual Symmetry Reductions and Interaction Solutions of (2+1)-Dimensional Burgers Equation

TL;DR

This paper explores symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation using residual symmetries, Lie group methods, and a new Bäcklund transformation to generate complex nonlinear solutions.

Contribution

It introduces a novel Bäcklund transformation and applies symmetry localization to derive new interaction solutions for the (2+1)-dimensional Burgers equation.

Findings

Derived new symmetry reduction solutions.

Established a new Bäcklund transformation.

Obtained interaction solutions among nonlinear excitations.

Abstract

The (2+1)-dimensional Burgers equation has been investigated first from prospective of symmetry by localizing the nonlocal residual symmetries and then studied by a simple generalized tanh expansion method. New symmetry reduction solutions has been obtained by using the standard Lie point symmetry group approach. A new B\"{a}klund transformation for Burgers equation has been given with the generalized tanh expansion method . From this BT, interactive solutions among different nonlinear excitations which is hard to obtain by other methods has also been obtained easily.