Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping
Exactly Solvable and Integrable Systems
2014-06-24 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1308.4265,
title = {Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping},
author = {Oleksandr A. Pocheketa and Roman O. Popovych and Olena O. Vaneeva},
journal= {arXiv preprint arXiv:1308.4265},
year = {2014}
}
Comments
18 pages, 1 figure; the version accepted to Appl. Math. Comput