2013/12/31 by Julia Bernatska, Petro Holod
Mathematics · Physics and Astronomy · #Algebraic number #Integrable system #Invertible matrix #Isotropy #Manifold (fluid mechanics) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Orbit (dynamics) #Quantum Mechanics and Non-Hermitian Physics #Separation of variables #math-ph #math.MP #msc:35Q51 #msc:37K10 #nlin.SI
paper · pdf · doi:10.1007/s00220-014-2176-9
published as Commun. Math. Phys. 333 (2015), 905-929 · 20 pages
arxiv created 2014/08/16 · openalex publication_date 2014/10/04 · arxiv updated 2016/11/03 · openalex created_date 2019/03/02 · openalex updated_date 2026/08/05
Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an \mathfraksl(3) loop algebra. We consider two types of generic orbits embedded into a common manifold, endowed with two nonsingular Lie-Poisson brackets. We prove that separation of variables on orbits of both types is realized by the same variables of separation. We also construct the integrable systems on these orbits: a coupled 3-component nonlinear Schrödinger equation and an isotropic SU(3) Landau-Lifshitz equation.