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Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization

100%

Golenia J., Hentosh O., Prykarpatsky A.

Open Mathematics

2007

tom 5

nr 1

84-104

The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.

A model of quotient spaces

100%

Hattab H.

Topological Algebra and its Applications

2017

tom 5

nr 1

13-18

Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.

Ograniczanie wyników

1 Open Mathematics

1 Topological Algebra and its Applications

1 Golenia J.

1 Hattab H.

1 Hentosh O.

1 Prykarpatsky A.

1 2017

1 2007

Wyniki wyszukiwania

Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization

A model of quotient spaces