Nonlinear systems of the Burgers-type equations: Lie and Q-conditional symmetries, Ansätze and solutions

A class of nonlinear diffusion–convection systems containing two Burgers-type equations is considered. A complete description of Lie symmetries is obtained for these systems. New results of finding Q-conditional symmetries are also presented. Moreover, a variety of Lie and non-Lie Ansätze and exact solutions of a diffusion–convection system invariant under the generalized Galilei algebra are constructed.  2003 Elsevier Science (USA). All rights reserved.