Conditional Lie-Bäcklund symmetry and reduction of evolution equations.

Details Conditional Lie-Bäcklund symmetry and reduction of evolution equations. Conditional Lie-Bäcklund symmetry and reduction of evolution equations.

1995-05-31

arxiv.org/abs/solv-int/9505006v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1088/0305-4470/28/13/027

We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-B\"acklund vector field. Such generalization proves to be effective and enables us to construct principally new Ans\"atze 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.

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