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.
|Number of pages||23|
|Journal||Theoretical and Mathematical Physics(Russian Federation)|
|Publication status||Published - Aug 2021|
- elliptic solutions
- Ruijsenaars–Schneider model
- Toda lattice hierarchy