Few remarks on Baecklund transformations for many-body systems

Details Few remarks on Baecklund transformations for many-body systems Few remarks on Baecklund transformations for many-body systems

1997-11-14

arxiv.org/abs/solv-int/9711010v1

J.Phys.A 31 (1998) 2241-2251

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, latex v.2.09, no figures

Scientific paper

10.1088/0305-4470/31/9/012

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 of the Baecklund transformations (BT's) from the Hamiltonian point of view. The analogy between BT and Baxter's quantum Q-operator pointed out by Pasquier and Gaudin is exploited to produce a conjugated variable mu for the parameter lambda of the BT B_lambda such that mu belongs to the spectrum of the Lax operator L(lambda). As a consequence, the generating function of the composition of n BT's gives rise also to another canonical transformation separating variables for the model. For the Toda lattice the dual BT parametrized by mu is introduced.

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