Lie Group Classification for a Reduced Burgers System

We consider a variable coefficient Burgers system in two spatial variables. A similarity mapping is used to reduce the number of independent variables. Lie symmetry analysis is applied to the reduced system. We present the equivalence groups for this system and the complete Lie group classification. Lie symmetries are employed to reduce the system into ordinary differential equations. In certain cases, we derive exact solutions. A special case of the system admits a hidden symmetry. Furthermore, a differential substitution is applied to this special system that enables us to construct additional exact solutions.