Integrable negative flows of the Heisenberg ferromagnet equation hierarchy

TL;DR

This paper explores the negative flows within the integrable Heisenberg ferromagnet hierarchy, linking them to the short pulse equation and providing methods to generate Lax pairs and soliton solutions.

Contribution

It introduces a framework for generating Lax pairs for negative flows and derives one-soliton solutions using inverse scattering and dressing methods.

Findings

Negative flows relate to the short pulse equation.

Framework for Lax pair generation for hierarchy members.

Explicit one-soliton solution derived.

Abstract

We study the negative flows of the hierarchy of the integrable Heisenberg Ferromagnet model and their soliton solutions. The first negative flow is related to the so-called short pulse equation. We provide a framework which generates Lax pairs for the other members of the hierarchy. The Inverse scattering, based on the dressing method is illustrated with the derivation of the one-soliton solution.