CONDITIONAL LIE-BACKLUND SYMMETRY AND REDUCTION OF EVOLUTION-EQUATIONS

Authors
Citation
Rz. Zhdanov, CONDITIONAL LIE-BACKLUND SYMMETRY AND REDUCTION OF EVOLUTION-EQUATIONS, Journal of physics. A, mathematical and general, 28(13), 1995, pp. 3841-3850
Citations number
17
Categorie Soggetti
Physics
ISSN journal
03054470
Volume
28
Issue
13
Year of publication
1995
Pages
3841 - 3850
Database
ISI
SICI code
0305-4470(1995)28:13<3841:CLSARO>2.0.ZU;2-Y
Abstract
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.