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/).
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 -