Completely integrable curve flows on Adjoint orbits

Simple item page
dc.creatorTerng, Chuu-Lian
dc.creatorThorbergsson, Gudlaugur
dc.date2001-08-22
dc.date.accessioned2026-07-07T04:43:05Z
dc.date.available2026-07-07T04:43:05Z
dc.descriptionIt 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.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0108154
dc.identifierhttp://arxiv.org/abs/math/0108154
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62063
dc.subjectDifferential Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.subject37K10, 37K25, 53C35
dc.titleCompletely integrable curve flows on Adjoint orbits
dc.typetext

Files

Collections

arXiv