CONDITIONAL LIE-BACKLUND SYMMETRY AND REDUCTION OF EVOLUTION-EQUATIONS

We suggest a generalization of the notion of invariance of a given par tial differential equation with respect to a Lie-Backlund vector field . Such a generalization proves to be effective and enables us to const ruct principally new ansatz reducing evolution-type equations to sever al ordinary differential equations. In the framework of the said gener alization, we obtain principally new reductions of a number of nonline ar heat conductivity equations u(t) = u(xx) + F(u, u(x)) with poor Lie symmetry and obtain their exact solutions. It is shown that these sol utions cannot be constructed by means of the symmetry reduction proced ure.