TY  - JOUR
ID  - Hentosh2007
LB  - Hentosh2007
AU  - Hentosh, Oksana Ye.
AU  - Prykarpatsky, Anatoliy K.
TI  - Integrable three-dimensional coupled nonlinear dynamical systems related with centrally extended operator Lie algebras
ST  - Integrable three-dimensional coupled nonlinear dynamical systems related with centrally extended operator Lie algebras
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2007
VL  - 27
IS  - 2
SP  - 231
EP  - 244
DO  - http://dx.doi.org/10.7494/OpMath.2007.27.2.231
UR  - http://dx.doi.org/10.7494/OpMath.2007.27.2.231
AB  - A hierarchy of Lax-type flows on a dual space to the centrally extended Lie algebra of integral-differential operators with matrix-valued coefficients is considered. By means of a specially constructed Backlund transformation the Hamiltonian representations for these flows coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems are obtained. The Hamiltonian description of the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax integrable \((3+1)\)-dimensional nonlinear dynamical systems and their triple Lax-type linearizations is analysed.
KW  - centrally extended operator Lie algebra
KW  - Lax-type flows
KW  - Backlund transformation
KW  - "ghost" symmetries
SN  - 1232-9274
ER  -