Geometric Bäcklund-Darboux transformations for the KP hierarchy

G.F. Helminck, J.W. van de Leur, J.W. van de Leur

Research output: Book/ReportReportProfessional

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Abstract

In this paper it is shown that, if you have two planes in the Sato Grassmannian that have an intersection of finite codimension, then the corresponding solutions of the KP hierarchy are linked by B\"acklund-Darboux (shortly BD-)transformations. The pseudodifferential operator that performs this transformation is shown to be built up in a geometric way from so-called elementary BD-transformations and is given here in a closed form. The corresponding action on the tau-function, associated to a plane in the Grassmannian, is also determined.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages33
Publication statusPublished - 2000

Publication series

NameMemorandum Faculteit TW
PublisherUniversity of Twente, Faculty of Applied Mathematics
No.1556
ISSN (Print)0169-2690

Keywords

  • MSC-22E70
  • EWI-3376
  • MSC-81R10
  • METIS-141313
  • MSC-58G37
  • IR-65743
  • MSC-22E65
  • MSC-22E67
  • MSC-35Q58
  • MSC-35Q53

Cite this

Helminck, G. F., van de Leur, J. W., & van de Leur, J. W. (2000). Geometric Bäcklund-Darboux transformations for the KP hierarchy. (Memorandum Faculteit TW; No. 1556). Enschede: University of Twente, Department of Applied Mathematics.
Helminck, G.F. ; van de Leur, J.W. ; van de Leur, J.W. / Geometric Bäcklund-Darboux transformations for the KP hierarchy. Enschede : University of Twente, Department of Applied Mathematics, 2000. 33 p. (Memorandum Faculteit TW; 1556).
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Helminck, GF, van de Leur, JW & van de Leur, JW 2000, Geometric Bäcklund-Darboux transformations for the KP hierarchy. Memorandum Faculteit TW, no. 1556, University of Twente, Department of Applied Mathematics, Enschede.

Geometric Bäcklund-Darboux transformations for the KP hierarchy. / Helminck, G.F.; van de Leur, J.W.; van de Leur, J.W.

Enschede : University of Twente, Department of Applied Mathematics, 2000. 33 p. (Memorandum Faculteit TW; No. 1556).

Research output: Book/ReportReportProfessional

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KW - MSC-22E70

KW - EWI-3376

KW - MSC-81R10

KW - METIS-141313

KW - MSC-58G37

KW - IR-65743

KW - MSC-22E65

KW - MSC-22E67

KW - MSC-35Q58

KW - MSC-35Q53

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Helminck GF, van de Leur JW, van de Leur JW. Geometric Bäcklund-Darboux transformations for the KP hierarchy. Enschede: University of Twente, Department of Applied Mathematics, 2000. 33 p. (Memorandum Faculteit TW; 1556).