Journal of Nonlinear Mathematical Physics

Volume 6, Issue 4, November 1995, Pages 411 - 447

r-Matrices for Relativistic Deformations of Integrable Systems

Authors
Yuri B. SURIS
Corresponding Author
Yuri B. SURIS
Available Online 1 November 1995.
DOI
https://doi.org/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).
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
6 - 4
Pages
411 - 447
Publication Date
1995/11
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1999.6.4.4How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Yuri B. SURIS
PY  - 1995
DA  - 1995/11
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  - https://doi.org/10.2991/jnmp.1999.6.4.4
ID  - SURIS1995
ER  -