Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping
arXiv:1308.4265 · doi:10.1016/j.amc.2014.05.099
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.
18 pages, 1 figure; the version accepted to Appl. Math. Comput
References in corpus (4)
- New results on group classification of nonlinear diffusion-convection equations
- Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
- Normalized classes of generalized Burgers equations
- Group classification of variable coefficient K(m,n) equations
Cited by in corpus (8)
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- Extended symmetry analysis of generalized Burgers equations
- Extended symmetry analysis of two-dimensional degenerate Burgers equation
- Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations
- Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
- Group classification of variable coefficient K(m,n) equations
- Solutions and reductions for radiative energy transport in laser-heated plasma
- Group analysis of Benjamin-Bona-Mahony equations with time dependent coefficients