$k$-symmetric AKS systems and flat immersions in spheres
| dc.creator | Brander, David | |
| dc.date | 2006-04-11 | |
| dc.date | 2008-02-03 | |
| dc.date.accessioned | 2026-07-07T12:23:50Z | |
| dc.date.available | 2026-07-07T12:23:50Z | |
| dc.description | We define a large class of integrable nonlinear PDE's, \emph{$k$-symmetric AKS systems}, whose solutions evolve on finite dimensional subalgebras of loop algebras, and linearize on an associated algebraic curve. We prove that periodicity of the associated algebraic data implies a type of quasiperiodicity for the solution, and show that the problem of isometrically immersing $n$-dimensional Euclidean space into a sphere of dimension $2n-1$ can be addressed via this scheme, producing infinitely many real analytic solutions. | |
| dc.description | 21 pages. Minor typographical corrections | |
| dc.identifier | https://arxiv.org/abs/math/0604245 | |
| dc.identifier | http://arxiv.org/abs/math/0604245 | |
| dc.identifier | J. London Math. Soc. (2) 77 (2008) 299-319 | |
| dc.identifier | doi:10.1112/jlms/jdm109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214131 | |
| dc.subject | Differential Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | 53C42; 37J35; 53C35 | |
| dc.title | $k$-symmetric AKS systems and flat immersions in spheres | |
| dc.type | text |