Journal of Nonlinear Mathematical Physics

Volume 2, Issue 1, February 1995

1. Non-linear Schrödinger Equations, Separation and Symmetry

George SVETLICHNY
Pages: 2 - 26
We investigate the symmetry properties of hierarchies of non-linear Schrödinger equations, introduced in [2], which describe non-interacting systems in which tensor product wave-functions evolve by independent evolution of the factors (the separation property). We show that there are obstructions to...

2. A Hopf C-algebra associated with an action of SUq(1,1) on a two-parameter quantum deformation of the unit disc

Yury CHAPOVSKY
Pages: 27 - 45
We define a Hopf C -algebra associated with an action of the quantum group SUq(1, 1) on a two-parameter quantum deformation of the unit disc, which has a left comodule structure over this Hopf C -algebra. Mathematics Subject Classification (1991). 81C05.

3. Geometrical symmetries of the Universal equation

V. DERJAGIN, A. LEZNOV
Pages: 46 - 50
It is shown that the group of geometrical symmetries of the Universal equation of D-dimensional space coincides with SL(D + 1, R).

5. Symmetry Reduction for Equation 2u + (u2 1 + u2 2 + u2 3)1/2 u0 = 0

L.F. BARANNYK, H.O. LAHNO
Pages: 73 - 89
The subalgebras of the invariance algebra of equation 2u+(u2

6. Non­Lie Ansatzes for Nonlinear Heat Equations

Ivan TSYFRA
Pages: 90 - 93
Operators of non­local symmetry are used to construct exact solutions of nonlinear heat equations. A method for finding of new classes of ansatzes reducing nonlinear wave equations to a systems of ordinary differential equations was suggested in [1]. This approach is based on non­local symmetry of differential...