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

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.