Elliptic spectral parameter and infinite dimensional Grassmann variety
| dc.creator | Takasaki, Kanehisa | |
| dc.date | 2003-12-08 | |
| dc.date | 2004-08-18 | |
| dc.date.accessioned | 2026-07-07T05:35:10Z | |
| dc.date.available | 2026-07-07T05:35:10Z | |
| dc.description | Recent results on the Grassmannian perspective of soliton equations with an elliptic spectral parameter are presented along with a detailed review of the classical case with a rational spectral parameter. The nonlinear Schrödinger hierarchy is picked out for illustration of the classical case. This system is formulated as a dynamical system on a Lie group of Laurent series with factorization structure. The factorization structure induces a mapping to an infinite dimensional Grassmann variety. The dynamical system on the Lie group is thereby mapped to a simple dynamical system on a subset of the Grassmann variety. Upon suitable modification, almost the same procedure turns out to work for soliton equations with an elliptic spectral parameters. A clue is the geometry of holomorphic vector bundles over the elliptic curve hidden (or manifest) in the zero-curvature representation. | |
| dc.description | Contribution to Faro conference "Infinite dimensional algebras and quantum integrable systems", latex2e, usepackage amssymb, 31pp, no figure; (v2) minor changes; (v3) final version for publication | |
| dc.identifier | https://arxiv.org/abs/nlin/0312016 | |
| dc.identifier | http://arxiv.org/abs/nlin/0312016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80618 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | Elliptic spectral parameter and infinite dimensional Grassmann variety | |
| dc.type | text |