ELLIPTIC SOLUTIONS OF THE TODA LATTICE HIERARCHY AND THE ELLIPTIC RUIJS']JSENAARS-SCHNEIDER MODEL

被引：3

作者：

Prokofev, V. V. ^{[1
,2
]}

Zabrodin, A., V ^{[2
,3
,4
]}

机构：

[1] Natl Res Univ, Moscow Inst Phys & Technol, Dolgoprudnyi, Moscow Region, Russia

[2] Skolkovo Inst Sci & Technol, Moscow, Russia

[3] Natl Res Univ Higher Sch Econ, Moscow, Russia

[4] Natl Res Ctr Kurchatov Inst, Alikhanov Inst Theoret & Expt Phys, Moscow, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2021年 / 208卷 / 02期

关键词：

Toda lattice hierarchy; Rui[!text type='js']js[!/text]enaars-Schneider model; elliptic solutions; INTEGRABLE SYSTEMS; EQUATION;

D O I：

10.1134/S0040577921080080

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider solutions of the 2D Toda lattice hierarchy that are elliptic functions of the "zeroth" time t(0) = x. It is known that their poles as functions of t1 move as particles of the elliptic RuijsenaarsSchneider 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 t(m) and (t) over bar (m) 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.

引用

页码：1093 / 1115

页数：23

共 23 条

[1] RATIONAL AND ELLIPTIC SOLUTIONS OF KORTEWEG DE-VRIES EQUATION AND A RELATED MANY-BODY PROBLEM [J].