Department of Applied Mathematics and Mathematical Modeling,

Kherson State Technical University,

Berislavs'ke Shosse 24, Kherson, UKRAINE

**Higher-order conditional symmetry and reduction of
systems of nonlinear evolution equations**

**Abstract:**

Reduction theorem for arbitrary systems of evolution equations admitting
higher-order conditional symmetries is formulated. Obtained results are
used for reduction of second and third order evolution equations and second
order systems of two evolution equations to systems of ordinary differential
equations. Some aspects of reduction of initial problems is considered
too.