SU(3) magnet: finite-gap integration on the lowest genus curve

Physics and Mathematics of Nonlinear Phenomena 2013

Bernatska, Julia^1 ; Holod, Petro^1

National University of 'Kyiv Mohyla Academy', G. Skovorody St., 2, 04655 Kyiv, Ukraine^1

关键词: Hamiltonian systems;    Integrable systems;    Landau-Lifshits equation;    Loop groups;    Mean field;    Quadrupole moments;    Separation of variables;    Spectral curves;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012004/pdf
DOI  :  10.1088/1742-6596/482/1/012004

来源: IOP

【 摘 要 】

We consider the integrable system of isotropic SU(3) Landau-Lifshits equation as a Hamiltonian system on a coadjoint orbit of the SU(3) loop group. We connect the mentioned equation with an isotropic SU(3) magnet because it describes the mean fields of magnetic and quadrupole moments in a spin-1 lattice. For the system of isotropic SU(3) Landau-Lifshits equation we perform separation of variables in Sklyanin's manner, and integrate in the lowest finite gap where the spectral curve is elliptic.