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

J. Golenia; O. Hentosh; A. Prykarpatsky

Open Mathematics (2007)

- Volume: 5, Issue: 1, page 84-104
- ISSN: 2391-5455

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topJ. Golenia, O. Hentosh, and A. Prykarpatsky. "Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization." Open Mathematics 5.1 (2007): 84-104. <http://eudml.org/doc/269031>.

@article{J2007,

abstract = {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.},

author = {J. Golenia, O. Hentosh, A. Prykarpatsky},

journal = {Open Mathematics},

keywords = {Three-dimensional Lax-type flows; R-matrix approach; integrable Hamiltonian systems; Backlund transformation; Lax-type flows; -matrix approach; Bäcklund transformation; Davey-Stewartson type systems},

language = {eng},

number = {1},

pages = {84-104},

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

url = {http://eudml.org/doc/269031},

volume = {5},

year = {2007},

}

TY - JOUR

AU - J. Golenia

AU - O. Hentosh

AU - A. Prykarpatsky

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

JO - Open Mathematics

PY - 2007

VL - 5

IS - 1

SP - 84

EP - 104

AB - 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.

LA - eng

KW - Three-dimensional Lax-type flows; R-matrix approach; integrable Hamiltonian systems; Backlund transformation; Lax-type flows; -matrix approach; Bäcklund transformation; Davey-Stewartson type systems

UR - http://eudml.org/doc/269031

ER -

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