Chopik V. I.
Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations
Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1433–1443
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.
Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 539–551
The nonlinear Schrödinger-type equations invariant with respect to the extended Galilean group are described. We study the conditional symmetry of such equations, realize the reduction procedure, and construct the classes of exact solutions.
Ukr. Mat. Zh. - 1991. - 43, № 11. - pp. 1504–1508