Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2021-04

Bjorn K. Berntson, Rob Klabbers, and Edwin Langmann


The non-chiral intermediate Heisenberg ferromagnet equation.



Abstract: We present and solve a soliton equation which we call the non-chiral intermediate Heisen- berg ferromagnet (ncIHF) equation. This equation, which depends on a parameter δ > 0, describes the time evolution of two coupled spin densities propagating on the real line, and in the limit δ → ∞ it reduces to two decoupled half-wave maps (HWM) equations of opposite chirality. We show that the ncIHF equation is related to the A-type hyperbolic spin Calogero- Moser (CM) system in two distinct ways: (i) it is obtained as a particular continuum limit of a Inozemtsev-type spin chain related to this CM system, (ii) it has multi-soliton solutions obtained by a spin-pole ansatz and with parameters satisfying the equations of motion of a complexified version of this CM system. The integrability of the ncIHF equation is shown by constructing a Lax pair. We also propose a periodic variant of the ncIHF equation related to the A-type elliptic spin CM system.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2021-04


50 pp.