EXCEPTIONAL SYMMETRY REDUCTIONS OF BURGERS-EQUATION IN 2 AND 3 SPATIAL DIMENSIONS

Lie point symmetry analysis of the general class of nonlinear diffusio n-convection equations in two and three dimensions has shown that only for Burgers' equation (that is D(u) = const, K(u) = quadratic) is a f ull symmetry reduction to an ordinary differential equation possible. The optimal system of symmetry operators is determined to ensure that a minimal complete set of reductions is obtained. For each reduced par tial differential equation, classical Lie group analysis has been perf ormed and further reductions obtained. In this manner, all possible re ductions to an ordinary differential equation are found, leading to ex act solutions to both the two and three dimensional Burgers' equation.