Elementary Darboux transformations for the $n$-component $KP$-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 a purely algebraic setting is described in which a characterization of the dual wavefunctions of the multicomponent $KP$-hierarchy and an interpretation of the bilinear form of this system of nonlinear equations can be given. The framework enables the construction of solutions starting from a matrix version of the Sato Grassmannian and the expression in formal power series determinants, the so-called $\tau$-functions. This leads to a geometric description of the elementary Darboux transformations for the $n$-component $KP$-hierarchy and one concludes with showing how to construct them, both at the differential operator level as at the $\tau$-function level.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages22
Publication statusPublished - 2002

Publication series

NameMemorandum Faculty Mathematical Sciences
PublisherUniversity of Twente, Department of Applied Mathematics
No.1645
ISSN (Print)0169-2690

Keywords

  • METIS-208643
  • MSC-22E65
  • MSC-35Q58
  • EWI-3465
  • MSC-58B25
  • IR-65831
  • MSC-22E70

Cite this

Helminck, G. F., van de Leur, J. W., & van de Leur, J. W. (2002). Elementary Darboux transformations for the $n$-component $KP$-hierarchy. (Memorandum Faculty Mathematical Sciences; No. 1645). Enschede: University of Twente, Department of Applied Mathematics.
Helminck, G.F. ; van de Leur, J.W. ; van de Leur, J.W. / Elementary Darboux transformations for the $n$-component $KP$-hierarchy. Enschede : University of Twente, Department of Applied Mathematics, 2002. 22 p. (Memorandum Faculty Mathematical Sciences; 1645).
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abstract = "In this paper a purely algebraic setting is described in which a characterization of the dual wavefunctions of the multicomponent $KP$-hierarchy and an interpretation of the bilinear form of this system of nonlinear equations can be given. The framework enables the construction of solutions starting from a matrix version of the Sato Grassmannian and the expression in formal power series determinants, the so-called $\tau$-functions. This leads to a geometric description of the elementary Darboux transformations for the $n$-component $KP$-hierarchy and one concludes with showing how to construct them, both at the differential operator level as at the $\tau$-function level.",
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Helminck, GF, van de Leur, JW & van de Leur, JW 2002, Elementary Darboux transformations for the $n$-component $KP$-hierarchy. Memorandum Faculty Mathematical Sciences, no. 1645, University of Twente, Department of Applied Mathematics, Enschede.

Elementary Darboux transformations for the $n$-component $KP$-hierarchy. / Helminck, G.F.; van de Leur, J.W.; van de Leur, J.W.

Enschede : University of Twente, Department of Applied Mathematics, 2002. 22 p. (Memorandum Faculty Mathematical Sciences; No. 1645).

Research output: Book/ReportReportProfessional

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AB - In this paper a purely algebraic setting is described in which a characterization of the dual wavefunctions of the multicomponent $KP$-hierarchy and an interpretation of the bilinear form of this system of nonlinear equations can be given. The framework enables the construction of solutions starting from a matrix version of the Sato Grassmannian and the expression in formal power series determinants, the so-called $\tau$-functions. This leads to a geometric description of the elementary Darboux transformations for the $n$-component $KP$-hierarchy and one concludes with showing how to construct them, both at the differential operator level as at the $\tau$-function level.

KW - METIS-208643

KW - MSC-22E65

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KW - EWI-3465

KW - MSC-58B25

KW - IR-65831

KW - MSC-22E70

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Helminck GF, van de Leur JW, van de Leur JW. Elementary Darboux transformations for the $n$-component $KP$-hierarchy. Enschede: University of Twente, Department of Applied Mathematics, 2002. 22 p. (Memorandum Faculty Mathematical Sciences; 1645).