rMatrices for Relativistic Deformations of Integrable Systems
Abstract
We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the rmatrix framework. An rmatrix account of the nonrelativistic lattice KP hierarchy is also provided for the reader's convenience. All relativistic constructions are regular oneparameter 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).
 Publication:

Journal of Nonlinear Mathematical Physics
 Pub Date:
 November 1999
 DOI:
 10.2991/jnmp.1999.6.4.4
 arXiv:
 arXiv:solvint/9906010
 Bibcode:
 1999JNMP....6..411S
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 J. Nonlinear Math. Phys. 6 (1999), no. 4, 411447