Institute of Mathematics, University of Bialystok,
ul. Akademicka 2, Bialystok, POLAND
E-mail: tsyfra@math.uwb.edu.pl
Institute of Geophysics of NAS of Ukraine,
32 Paladina Ave., Kyiv, UKRAINE
E-mail: tsyfra@igph.kiev.ua

Classical and conditional symmetry reductions of nonlinear evolution and wave equations

We consider different types of symmetry reductions of partial differential equations to equations with fewer number of independent variables. We have found the generalised sufficient conditions for the solution obtained with the help of conditional symmetry operators to be invariant in the classical sense.