Elliptic families of solutions to constrained Toda hierarchy

TL;DR

This paper investigates elliptic solutions to the constrained Toda hierarchy, deriving equations of motion for the poles of these solutions, and expanding understanding of their structure within integrable systems.

Contribution

It introduces elliptic families of solutions to the constrained Toda hierarchy and derives their pole dynamics equations, advancing the analytical understanding of these solutions.

Findings

Elliptic solutions are characterized as functions of linear combinations of hierarchical times.

Equations of motion for the poles of these solutions are explicitly derived.

The study enhances the theoretical framework of integrable systems with elliptic solutions.

Abstract

We study elliptic families of solutions to the recently introduced constrained Toda hierarchy, i.e., solutions which are elliptic functions of some linear combination of the hierarchical times. Equations of motion for poles of such solutions are obtained.