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

Published online by Cambridge University Press:  20 November 2018

G. F. Helminck  and
J. W. van de Leur
G. F. Helminck
Affiliation:
Faculty of Applied Mathematics University of Twente P.O.Box 217 7500 AE Enschede The Netherlands, email: helminck@math.utwente.nl
J. W. van de Leur
Affiliation:
Faculty of Mathematics University of Utrecht P.O.Box 80010 3508 TA Utrecht The Netherlands, email: vdleur@math.uu.nl
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Abstract

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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.

Keywords

22E6522E7035Q5335Q5858B25KP hierarchyDarboux transformationGrassmann manifold
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 2 , 01 April 2001 , pp. 278 - 309
Copyright
Copyright © Canadian Mathematical Society 2001

References

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