ISSN:
1572-9036
Keywords:
22E65
;
14M15
;
35Q58
;
43A80
;
17B65
;
infinite-dimensional flag varieties
;
modified equations
;
Darboux transforms
;
integrable deformations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we present several instances where infinite-dimensional flag varieties and their holomorphic line bundles play a role in integrable systems. As such, we give the correspondence between flag varieties and Darboux transformations for the KP hierarchy and the nth KdV hierarchy. We construct solutions of the nth MKdV hierarchy from the space of periodic flags and we treat the geometric interpretation of the Miura transform. Finally, we show how the group extension connected with these line bundles shows up at integrable deformations of linear systems on ℙ1(ℂ).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00996107
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