Elliptic spectral parameter and infinite dimensional Grassmann variety
Takasaki, Kanehisa
arXiv, 0312016 / Harvested from arXiv
Text on arXiv
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 Schr\"odinger 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.
Publié le : 2003-12-08
Classification:  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  High Energy Physics - Theory,  Mathematical Physics 
@article{0312016,
     author = {Takasaki, Kanehisa},
     title = {Elliptic spectral parameter and infinite dimensional Grassmann variety},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312016}
}

Takasaki, Kanehisa. Elliptic spectral parameter and infinite dimensional Grassmann variety. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312016/