Conditional Lie-Backlund symmetry and reduction of evolution equations

作者：Renat Zhdanov · 发表于：Journal of Physics A Mathematical and General · 年份：1995 · DOI：10.1088/0305-4470/28/13/027 · 被引用次数：190 · 研究领域：Nonlinear Waves and Solitons、Nonlinear Photonic Systems、Numerical methods for differential equations

We suggest a generalization of the notion of invariance of a given partial differential equation with respect to a Lie-Backlund vector field. Such a generalization proves to be effective and enables us to construct principally new ansatz 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 cannot be constructed by means of the symmetry reduction procedure.