Volume 6, Issue 4, November 1995, Pages 411 - 447
r-Matrices for Relativistic Deformations of Integrable Systems
Yuri B. SURIS
Yuri B. SURIS
Available Online 1 November 1995.
- https://doi.org/10.2991/jnmp.19184.108.40.206How to use a DOI?
- 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).
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- 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.19220.127.116.11 DO - https://doi.org/10.2991/jnmp.1918.104.22.168 ID - SURIS1995 ER -