Darboux Transformations for the KP Hierarchy in the Segal-Wilson Setting

Helminck, G. F. ; Leur, J. W. van de

Canadian journal of mathematics, Tome 53 (2001) no. 2, pp. 278-309

Résumé

In this paper it is shown that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the $\text{KP}$ hierarchy corresponding to these planes. We present a closed form of the operators that procure the transformation and express them in the related geometric data. Further the associated transformation on the level of $\tau $ -functions is given.

Détail

DOI : 10.4153/CJM-2001-012-4

Mots-clés : 22E65, 22E70, 35Q53, 35Q58, 58B25, KP hierarchy, Darboux transformation, Grassmann manifold

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