Elliptic solutions of the Toda lattice hierarchy and the elliptic Ruijsenaars–Schneider model

V. V. Prokofev, A. V. Zabrodin

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1 Citation (Scopus)

Abstract

Abstract: We consider solutions of the 2D Toda lattice hierarchy that are elliptic functions of the “zeroth” time t0=x. It is known that their poles as functions of t1 move as particles of the elliptic Ruijsenaars–Schneider model. The goal of this paper is to extend this correspondence to the level of hierarchies. We show that the Hamiltonians that govern the dynamics of poles with respect to the mth hierarchical times tm and (Formula presented.) of the 2D Toda lattice hierarchy are obtained from the expansion of the spectral curve for the Lax matrix of the Ruijsenaars–Schneider model at the marked points.

Original languageEnglish
Pages (from-to)1093-1115
Number of pages23
JournalTheoretical and Mathematical Physics(Russian Federation)
Volume208
Issue number2
DOIs
Publication statusPublished - Aug 2021

Keywords

  • elliptic solutions
  • Ruijsenaars–Schneider model
  • Toda lattice hierarchy

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