2001/08/22 by Chuu-Lian Terng, Terng, Chuu-Lian, Gudlaugur Thorbergsson +1
Mathematics · Physics and Astronomy · #37K10 #37K25 #53C35 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.DG #msc:37K10 #msc:37K25 #msc:53C35 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0108154
25 pages
arxiv created 2001/08/22 · openalex publication_date 2001/08/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the n-wave equation. In this paper, we give a systematic method to construct integrable geometric curve flows on Adjoint U-orbits from flows in the soliton hierarchy associated to a compact Lie group U. There are natural geometric bi-Hamiltonian structures on the space of curves on Adjoint orbits, and they correspond to the order two and three Hamiltonian structures on soliton equations under our construction. We study the Hamiltonian theory of these geometric curve flows and also give several explicit examples.