On canonical variables in integrable models of magnets

TL;DR

This paper explores three integrable magnet models using stereographic projection, deriving their Hamiltonians, analyzing solution stability, and calculating topological charges to deepen understanding of their mathematical structure and physical properties.

Contribution

It provides explicit Hamiltonians, stability analysis, and topological charge calculations for the deformed Heisenberg, Landau-Lifshitz, and Ishimori magnet models, advancing their theoretical understanding.

Findings

Stability of solitons in the Heisenberg magnet is analyzed.

Stationary solutions for the Landau-Lifshitz magnet are obtained.

Hamiltonians and topological charges for the Ishimori model are calculated.

Abstract

Three integrable models - the deformed Heisenberg, Landau - Lifschits and Ishimori magnets are written in terms of the stereographic projection. The Hamiltonians of these models are obtained and certain questions related to the existence of exact solutions are studied. In particular, the stability of solitions is studied for the Heisenberg marnet, simplest stationary solutions are obtained for the Landau - Lifschits magnet, and Hamiltonians and topological charges are calculated for several known solutions of the Ishimori model