Time discretization of the deformed Ruijsenaars-Schneider system
A. Zabrodin
TL;DR
This paper develops integrable time discretization and Bäcklund transformations for the deformed Ruijsenaars-Schneider system, linking it to elliptic solutions of the Toda lattice and discrete KP equations, and proposes a field analogue on a lattice.
Contribution
It introduces a novel integrable time discretization and Bäcklund transformations for the deformed Ruijsenaars-Schneider system, connecting it to elliptic solutions of related integrable equations.
Findings
Discrete-time deformed Ruijsenaars-Schneider system as poles of elliptic solutions
Connection to fully discrete KP equation of type B
Proposal of a field analogue on a space-time lattice
Abstract
We obtain B\"acklund transformations and integrable time discretization of the recently introduced deformed Ruijsenaars-Schneider many-body system which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint of type B. We also show that the deformed Ruijsenaars-Schneider system in discrete time is the dynamical system for poles of elliptic solutions to the fully discrete Kadomtsev-Petviashvili equation of type B. Besides, we suggest a field analogue of the deformed Ruijsenaars-Schneider system on a space-time lattice.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Molecular spectroscopy and chirality