On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations

For a system of two partial differential equations in two independent variables the Lie point symmetry generator has the form τ(t,x,u,v)∂t+ξ(t,x,u,v)∂x+η(t,x,u,v)∂u+μ(t,x,u,v)∂v. We consider a system of evolution equations of general class and we provide restrictions on the functional forms of the coefficient functions of the Lie generator. These restrictions reduce the amount of calculations in determining the Lie symmetries of the system under study. We show that τ=τ(t) except in one special case and we present further restrictions on the remaining coefficient functions.