Structures in BCN Ruijsenaars-Schneider models
J. Avan, G. Rollet
Abstract
We construct the classical r-matrix structure for the Lax formulation of BCN Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the AN Ruijsenaars-Schneider Poisson bracket behavior, although the dynamical dependence is more complicated. Commuting Hamiltonians stemming from the BCN Ruijsenaars-Schneider Lax matrix are shown to be linear combinations of particular Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings. Uniqueness of such commuting Hamiltonians is established once the first of them and the general analytic structure are given.
Create a lesson
Related papers
Integrability of the deformed Toda systems
Mikhail Vasilev
An integrable Z22-graded extension of Camassa-Holm equation and its bi-Hamiltonian structure
N. Aizawa, Ichi Fujii, Ren Ito et al.
Maxwell's relations as Hamilton's equations: a symplectic and variational framework
Sikarin Yoo-Kong
The Nakamura Conjecture Revisited: Toda Molecules and Stationary Axisymmetric Gravity
Takeshi Fukuyama
Multivariable Painleve'-II equation: connection formulas for arbitrary system size
Nikolai A. Sinitsyn
Vector rogue wave patterns associated with generalized Hermite and Okamoto polynomials
Hejiaqi Chen, Dongwei Wu, Chengfa Wu et al.