Умовна симетрія та нові зображення алгебри Галілея для нелінійних рівнянь параболічного типу

Abstract

An effective method for finding conditional symmetry operators is construcled for a class of Galilei non-invaiiant parabolic equations. The obtained opcrators fonn a basis of the Galilei algebra. The additional conditions, under which the extension of a symmetry is possible, arc obtained. For the equations under consideration, the antireduction is carried out and some exact solutions are found by using the conditional Galilei-invariance of its differentiel consequences.