Toda lattice hierarchy and trigonometric Ruijsenaars-Schneider hierarchy

V. Prokofev, A. Zabrodin

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1 Citation (Scopus)


We consider solutions of the 2D Toda lattice hierarchy, which are trigonometric functions of the 'zeroth' time t 0 = x. It is known that their poles move as particles of the trigonometric Ruijsenaars-Schneider model. We extend this correspondence to the level of hierarchies: the dynamics of poles with respect to the mth hierarchical time tm (respectively, tm) of the 2D Toda lattice hierarchy is shown to be governed by the Hamiltonian which is proportional to the mth Hamiltonian tr Lm (respectively, tr L-m) of the Ruijsenaars-Schneider model, where L is the Lax matrix.

Original languageEnglish
Article number495202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number49
Publication statusPublished - 11 Nov 2019


  • dynamics of poles
  • Ruijsenaars Schneider system
  • Toda lattice hierarchy


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