Conditional Lie-Bäcklund symmetry and reduction of evolution equations.

Abstract

We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-Bäcklund vector field. Such generalization proves to be effective and enables us to construct principally new Ansätze reducing evolution-type equations to several ordinary differential equations. In the framework of the said generalization we obtain principally new reductions of a number of nonlinear 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 solutions can not be constructed by means of the symmetry reduction procedure.

12 pages, latex, needs amssymb., to appear in the "Journal of Physics A: Mathematical and General" (1995)

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