Higher Conditional Symmetries and Reduction of Initial Value Problems for Nonlinear Evolution Equations

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

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