dorsal/arxiv
View SchemaFew remarks on Baecklund transformations for many-body systems
| Authors | V. B. Kuznetsov, E. K. Sklyanin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9711010 |
| URL | https://arxiv.org/abs/solv-int/9711010 |
| DOI | 10.1088/0305-4470/31/9/012 |
| Journal | J.Phys.A 31 (1998) 2241-2251 |
Abstract
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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"abstract": "Using the n-particle periodic Toda lattice and the relativistic\ngeneralization due to Ruijsenaars of the elliptic Calogero-Moser system as\nexamples, we revise the basic properties of the Baecklund transformations\n(BT\u0027s) from the Hamiltonian point of view. The analogy between BT and Baxter\u0027s\nquantum Q-operator pointed out by Pasquier and Gaudin is exploited to produce a\nconjugated variable mu for the parameter lambda of the BT B_lambda such that mu\nbelongs to the spectrum of the Lax operator L(lambda). As a consequence, the\ngenerating function of the composition of n BT\u0027s gives rise also to another\ncanonical transformation separating variables for the model. For the Toda\nlattice the dual BT parametrized by mu is introduced.",
"arxiv_id": "solv-int/9711010",
"authors": [
"V. B. Kuznetsov",
"E. K. Sklyanin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/31/9/012",
"journal_ref": "J.Phys.A 31 (1998) 2241-2251",
"title": "Few remarks on Baecklund transformations for many-body systems",
"url": "https://arxiv.org/abs/solv-int/9711010"
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