Andrij Andreytsev (Kyiv University of Transport Economy and Technologies, Ukraine)

Classification and reduction of initial-value problems for nonlinear evolution equations, admitting three-order conditional symmetries

Abstract:
Algorithm for construction of conditionally invariant evolution equations and their reduction to the systems of ordinary differential equations is suggested. Classification and reduction theorem is formulated for n-order evolution equations. Classification and reduction of initial-value problems for second order evolution equations to the Cauchi problems for system of three ordinary differential equations is carried out.