منابع مشابه
The D n Ruijsenaars - Schneider model
The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears...
متن کاملRuijsenaars-Schneider models and their spectral curves
We study the elliptic Cn and BCn Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameterized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the syst...
متن کاملStructures in Bc N Ruijsenaars-schneider Models
We construct the classical r-matrix structure for the Lax formulation of BC N Ruijsenaars-Schneider systems proposed in [18]. The r-matrix structure takes a quadratic form similar to the A N Ruijsenaars-Schneider Poisson bracket behavior, although the dy-namical dependence is more complicated. Commuting Hamiltonians stemming from the BC N Ruijsenaars-Schneider Lax matrix are shown to be linear ...
متن کاملRuijsenaars-schneider Models and Their Spectral Curves
We study the elliptic C n and BC n Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameter-ized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the s...
متن کاملRational Ruijsenaars-schneider Hierarchy and Bispectral Difference Operators
Abstract. We show that a monic polynomial in a discrete variable n, with coefficients depending on time variables t1, t2, . . . is a τ -function for the discrete Kadomtsev-Petviashvili hierarchy if and only if the motion of its zeros is governed by a hierarchy of Ruijsenaars-Schneider systems. These τ -functions were considered in [10], where it was proved that they parametrize rank one solutio...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2015
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.114.121602