Systems of PDEs obtained from factorization in loop groups
| dc.creator | Dorfmeister, J. | |
| dc.creator | Gradl, H. | |
| dc.creator | Szmigielski, J. | |
| dc.date | 1998-01-08 | |
| dc.date.accessioned | 2026-07-07T06:17:30Z | |
| dc.date.available | 2026-07-07T06:17:30Z | |
| dc.description | We propose a generalization of a Drinfeld-Sokolov scheme of attaching integrable systems of PDEs to affine Kac-Moody algebras. With every affine Kac-Moody algebra $\gg$ and a parabolic subalgebra $\gp$, we associate two hierarchies of PDEs. One, called positive, is a generalization of the KdV hierarchy, the other, called negative, generalizes the Toda hierarchy. We prove a coordinatization theorem, which establishes that the number of functions needed to express all PDEs of the the total hierarchy equals the rank of $\gg$. The choice of functions, however, is shown to depend in a noncanonical way on $\gp$. We employ a version of the Birkhoff decomposition and a ``2-loop'' formulation which allows us to incorporate geometrically meaningful solutions to those hierarchies. We illustrate our formalism for positive hierarchies with a generalization of the Boussinesq system and for the negative hierarchies with the stationary Bogoyavlenskii equation. | |
| dc.description | 1 figure | |
| dc.identifier | https://arxiv.org/abs/solv-int/9801009 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9801009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94409 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Systems of PDEs obtained from factorization in loop groups | |
| dc.type | text |