Solitons in a continuous classical Haldane-Shastry spin chain

TL;DR

This paper discovers and analyzes soliton solutions in a continuum classical Haldane-Shastry spin chain, revealing their topological nature and collision resilience, thus advancing understanding of integrable spin models.

Contribution

It provides the first analytic multi-lump soliton solutions in a continuum Haldane-Shastry model and demonstrates their stability through numerical collision experiments.

Findings

Analytic multi-lump soliton solutions found

Solitons exhibit topological features

Solitons survive collisions, indicating multi-soliton solutions

Abstract

Motivated by Polychronakos' discovery that solitons exist in the hydrodynamic equations of continuum version of the Calogero model, we seek solitons in the classical dynamics of a continuum version of the Haldane-Shastry spin chain. We have obtained analytic multi-lump solitary wave solutions for our spin-field equation, and these solutions possess interesting topological features. We have performed numerical collision experiments showing that these solitary waves survive collisions, and thus suggest the existence of true multi-soliton solutions.