7 papers
Quantum Backlund transformation for the integrable DST model
V. B. Kuznetsov, M. Salerno, E. K. Sklyanin
For the integrable case of the discrete self-trapping (DST) model we construct a Backlund transformation. The dual Lax matrix and the corresponding dual Backlund transformation are…
Few remarks on Baecklund transformations for many-body systems
V. B. Kuznetsov, E. K. Sklyanin
Using the n-particle periodic Toda lattice and the relativistic generalization due to Ruijsenaars of the elliptic Calogero-Moser system as examples, we revise the basic properties…
Separation of variables for the Ruijsenaars system
V. B. Kuznetsov, F. W. Nijhoff, E. K. Sklyanin
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates ap…
Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
F. W. Nijhoff, V. B. Kuznetsov, E. K. Sklyanin +1
The classical r-matrix structure for the generic elliptic Ruijsenaars-Schneider model is presented. It makes the integrability of this model as well as of its discrete-time version…
New boundary conditions for integrable lattices
V. B. Kuznetsov, M. F. Jorgensen, P. L. Christiansen
New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulat…
Separation of variables and the XXZ Gaudin magnet
E. G. Kalnins, V. B. Kuznetsov, Willard Miller
In this work we generalise previous results connecting (rational) Gaudin magnet models and classical separation of variables. It is shown that the connection persists for the case…