Geodesic
On integrability of the deformed Ruijsenaars--Schneider system
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 2, pp. 349-386

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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 the 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. We also obtain Bäcklund transformations and integrable time discretization of the deformed Ruijsenaars–Schneider system, which is shown to be the dynamical system for poles of elliptic solutions to the fully discrete Kadomtsev–Petviashvili equation of type B. In additon, we propose a field analogue of the deformed Ruijsenaars–Schneider system on a space-time lattice. Bibliography: 35 titles.
Keywords: Ruijsenaars–Schneider system, integrable systems, integrals of motion, discrete time. 
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     title = {On integrability of the deformed {Ruijsenaars--Schneider} system},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     url = {http://geodesic.mathdoc.fr/item/RM_2023_78_2_a2/}
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A. V. Zabrodin. On integrability of the deformed Ruijsenaars--Schneider system. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 2, pp. 349-386. http://geodesic.mathdoc.fr/item/RM_2023_78_2_a2/