Journal of Nonlinear Mathematical Physics

Volume 6, Issue 4, November 1999, Pages 411 - 447

r-Matrices for Relativistic Deformations of Integrable Systems

Authors
Yuri B. Suris
Corresponding Author
Yuri B. Suris
Received 6 June 1999, Revised 5 July 1999, Accepted 5 August 1999, Available Online 1 November 1999.
DOI
10.2991/jnmp.1999.6.4.4How to use a DOI?
Abstract

We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the r-matrix framework. An r-matrix account of the nonrelativistic lattice KP hierarchy is also provided for the reader's convenience. All relativistic constructions are regular one-parameter perturbations of the nonrelativistic ones. We derive in a simple way the linear Hamiltonian structure of the relativistic lattice KP, and find for the first time its quadratic Hamiltonian structure. Amasingly, the latter turns out to coincide with its nonrelativistic counterpart (a phenomenon, known previously only for the simplest case of the relativistic Toda lattice).

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
6 - 4
Pages
411 - 447
Publication Date
1999/11/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.1999.6.4.4How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Yuri B. Suris
PY  - 1999
DA  - 1999/11/01
TI  - r-Matrices for Relativistic Deformations of Integrable Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 411
EP  - 447
VL  - 6
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.4.4
DO  - 10.2991/jnmp.1999.6.4.4
ID  - Suris1999
ER  -