LIE SYMMETRIES OF A COUPLED NONLINEAR BURGERS HEAT-EQUATION SYSTEM

A symmetry group analysis of a coupled Burgers-heat equation system of partial differential equations initially introduced in a study of non-classical similarity solutions of the heat equation is carried out. The point Lie algebra of the system G, is shown to possess a maximal solvable ideal A with quotient algebra B=G/A approximately=sl2(R), where sl2(R) is the Lie algebra of 2*2 matrices with zero trace. Analysis of the prolongation structure of the system yields the Backlund transformation obtained previously by Painleve analysis. The Backlund transformation can be expressed as a map onto two coupled linear heat equations, or alternatively as a map onto Burgers equation. The role of sl2 (R) in a seven-dimensional Lie algebra, L1, obtained by truncating the open-ended algebraic prolongation structure is emphasised.