Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1998-09-02
Nonlinear Sciences
Exactly Solvable and Integrable Systems
plain LaTeX, 28 pages
Scientific paper
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a generalization of an integrable case of the H\'enon-Heiles system. We give a Lax representation in terms of $2\times 2$ matrices for the whole hierarchy and construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A Yang-Baxter equation of dynamical type is proposed. Classical integration in a particular case is carried out and quantization of the system is discussed with the help of separation variables. This paper was published in the rary issues: Sfb 288 Preprint No. 110, Berlin and Nonlinear Mathematical Physics, {\bf 1(3)}, 275-294 (1994)
Eilbeck Chris J.
Enol'skii V. Z.
Kuznetsov Vadim B.
Leykin D. V.
No associations
LandOfFree
Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-264082