Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics

TL;DR

This paper constructs explicit periodic solutions for the non-chiral intermediate Heisenberg ferromagnet equation using elliptic functions, linking them to an elliptic spin Calogero-Moser system and introducing a new Bäcklund transformation.

Contribution

The authors derive exact periodic solutions of the ncIHF equation via a spin-pole ansatz and establish a novel Bäcklund transformation for the associated elliptic spin Calogero-Moser system.

Findings

Solutions expressed through elliptic functions

Dynamical parameters satisfy an elliptic spin CM system

Introduction of a new Bäcklund transformation for the system

Abstract

We present a class of periodic solutions of the non-chiral intermediate Heisenberg ferromagnet (ncIHF) equation, which was recently introduced by the authors together with Langmann as a classical, continuum limit of an Inozemtsev-type spin chain. These exact analytic solutions are constructed via a spin-pole ansatz written in terms of certain elliptic functions. The dynamical parameters in our solutions solve an elliptic spin Calogero-Moser (CM) system subject to certain constraints. In the course of our construction, we establish a novel B\"acklund transformation for this constrained elliptic spin CM system.