2019
Том 71
№ 6

All Issues

Chopik V. I.

Articles: 3
Article (Ukrainian)

Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations

Chopik V. I., Fushchich V. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Symmetry and non-lie reduction of the nonlinear Schrödinger equation

Chopik V. I., Fushchich V. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Non-Lie reduction of nonlinear Schrodinger equation

Chopik V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 11. - pp. 1504–1508