Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations
An efficient method for finding operators of conditional symmetry, which form a basis of the Galilean algebra, is suggested for a class of Galilei noninvariant parabolic equations. Additional conditions, under which the symmetry can be extended, are described. For the nonlinear equation under consideration, the antireduction is realized and some exact solutions are found by using the conditional Galilei invariance of its differential consequences.
English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 10, pp 1609-1622.
Citation Example: Chopik V. I., Fushchich V. I. Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations // Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1433–1443.