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

摘要

Admissible point transformations between Burgers equations with lineardamping and time-dependent coefficients are described and used in order toexhaustively classify Lie symmetries of these equations. Optimal systems ofone- and two-dimensional subalgebras of the Lie invariance algebras obtainedare constructed. The corresponding Lie reductions to ODEs and to algebraicequations are carried out. Exact solutions to particular equations are found.Some generalized Burgers equations are linearized to the heat equation bycomposing equivalence transformations with the Hopf-Cole transformation.