6533b859fe1ef96bd12b6e18
RESEARCH PRODUCT
Stationary problems for equation of the KdV type and dynamical r-matrices
Andrey Vladimirovich TsiganovP. P. KulishS. Rauchwojciechowskisubject
PhysicsHigh Energy Physics - TheoryLoop algebraIntegrable systemStructure (category theory)FOS: Physical sciencesStatistical and Nonlinear PhysicsType (model theory)Hamiltonian systemSet (abstract data type)Nonlinear Sciences::Exactly Solvable and Integrable SystemsHigh Energy Physics - Theory (hep-th)Quartic functionKorteweg–de Vries equationMathematical PhysicsMathematical physicsdescription
We study a quite general family of dynamical $r$-matrices for an auxiliary loop algebra ${\cal L}({su(2)})$ related to restricted flows for equations of the KdV type. This underlying $r$-matrix structure allows to reconstruct Lax representations and to find variables of separation for a wide set of the integrable natural Hamiltonian systems. As an example, we discuss the Henon-Heiles system and a quartic system of two degrees of freedom in detail.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-03-10 |