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Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System

Mathematical Physics Analysis and Geometry. 2023. Vol. 26. No. 3. Article 20.
Prokofiev V., Zabrodin A.

We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars-Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By studying more general elliptic solutions (elliptic families), we also suggest an extension of the deformed Ruijsenaars-Schneider system to a field theory.

Research target: Mathematics
Language: English
DOI
Keywords: Toda latticeelliptic functionsRuijsenaars–Schneider systemKeywords Integrable systemsField equations
Publication based on the results of:
Representation theory of W-algebras affine and toroidal quantum groups and its applications to geometry, topology and combinatorics (2023)
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