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

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 Bäcklund transformation for this constrained elliptic spin CM system.

arXiv comment37 pages, 3 figures

References in corpus (17)

• Lattice Integrable Systems of Haldane-Shastry Type
• A route to thermalization in the $\alpha$-Fermi-Pasta-Ulam system
• Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• On energy-critical half-wave maps into ${\mathbb{S}}^2$
• Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems
• A Lax Pair Structure for the Half-Wave Maps Equation
• Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
• Spin generalizations of the Benjamin-Ono equation
• Solitons in a continuous classical Haldane-Shastry spin chain
• On the non-chiral intermediate long wave equation II: periodic case
• Collective Field Description of Spin Calogero-Sutherland Models
• The non-chiral intermediate Heisenberg ferromagnet equation
• Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation
• Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation
• Derivation of the Half-Wave Maps Equation from Calogero--Moser Spin Systems
• The Lax pair structure for the spin Benjamin--Ono equation

Cited by in corpus (1)

• Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation