Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping

TL;DR

This paper classifies symmetries of variable-coefficient Burgers equations with damping, constructs optimal subalgebra systems, performs reductions, and finds exact solutions, including linearizations to the heat equation.

Contribution

It provides a comprehensive symmetry classification and solution methods for a class of variable-coefficient Burgers equations with damping, extending previous analyses.

Findings

Lie symmetry classifications of the equations.

Explicit exact solutions for particular cases.

Linearization to the heat equation via transformations.

Abstract

Admissible point transformations between Burgers equations with linear damping and time-dependent coefficients are described and used in order to exhaustively classify Lie symmetries of these equations. Optimal systems of one- and two-dimensional subalgebras of the Lie invariance algebras obtained are constructed. The corresponding Lie reductions to ODEs and to algebraic equations are carried out. Exact solutions to particular equations are found. Some generalized Burgers equations are linearized to the heat equation by composing equivalence transformations with the Hopf-Cole transformation.