On integrability of the deformed Ruijsenaars-Schneider system
A. Zabrodin
TL;DR
This paper discovers integrals of motion for a deformed Ruijsenaars-Schneider system, linking it to elliptic solutions of the Toda lattice with type B constraints, revealing new integrability properties.
Contribution
It introduces a novel method to find integrals of motion for the deformed system by relating it to pairs of Ruijsenaars-Schneider particles.
Findings
Identified integrals of motion for the deformed system
Connected the system's equations to pairs of particles maintaining fixed distances
Enhanced understanding of the system's integrability
Abstract
We find integrals of motion for 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. Our method is based on the fact that equations of motion for this system coincide with those for pairs of Ruijsenaars-Schneider particles which stick together preserving a special fixed distance between the particles.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics