Alla VOROBYOVA
Mykolayiv Petro Mogyla State Humanities University,
Mykolaiv, UKRAINE
E-mail: alla@mksat.net, leifura@kma.mk.ua

Sets of conditional symmetry operators and exact solutions for wave and generalised heat equations

Abstract:
Reduction of some wave and heat equations by means of ansatzes in special coordinate systems results in ODEs with additional symmetry operators compared to original ones. Such operators will allow constructing sets of conditional symmetry operators that represent hidden symmetry of the equations. Classes of generalised wave and heat equations possessing these symmetry properties are described, and families of respective nonclassical solutions are listed.