Highly Influenced

7 Excerpts

@inproceedings{Zhdanov2000HigherCS, title={Higher Conditional Symmetries and Reduction of Initial Value Problems for Nonlinear Evolution Equations}, author={Renat Z. Zhdanov}, year={2000} }

- Published 2000

We prove that the presence of higher conditional symmetry is the necessary and sufficient condition for reduction of an arbitrary evolution equation in two variables to a system of ordinary differential equations. Furthermore, we give the sufficient condition for an initial value problem for an evolution equation to be reducible to a Cauchy problem for a system of ordinary differential equations, provided it possesses higher conditional symmetry.