R-matrices for relativistic deformations of integrable systems

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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).

Original languageEnglish
Pages (from-to)411-447
Number of pages37
JournalJournal of Nonlinear Mathematical Physics
Volume6
Issue number4
DOIs
StatePublished - 1999
Externally publishedYes

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