Geometric Bäcklund-Darboux transformations for the KP-hierarchy

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

    Research output: Contribution to journalArticleAcademicpeer-review

    9 Citations (Scopus)
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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 Bäcklund-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
    Pages (from-to)479-519
    JournalResearch institute for mathematical sciences. Publications
    Volume37
    Issue number4
    DOIs
    Publication statusPublished - 2001

    Keywords

    • Toda lattice hierarchy
    • KP hierarchy
    • IR-70361
    • Bäcklund-Darboux transformation
    • METIS-202028
    • Constrained KP
    • Grassmann manifold

    Cite this

    Helminck, G.F. ; van de Leur, J.W. ; van de Leur, Johan W. / Geometric Bäcklund-Darboux transformations for the KP-hierarchy. In: Research institute for mathematical sciences. Publications. 2001 ; Vol. 37, No. 4. pp. 479-519.
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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{\"a}cklund-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.",
    keywords = "Toda lattice hierarchy, KP hierarchy, IR-70361, B{\"a}cklund-Darboux transformation, METIS-202028, Constrained KP, Grassmann manifold",
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    Geometric Bäcklund-Darboux transformations for the KP-hierarchy. / Helminck, G.F.; van de Leur, J.W.; van de Leur, Johan W.

    In: Research institute for mathematical sciences. Publications, Vol. 37, No. 4, 2001, p. 479-519.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AU - van de Leur, J.W.

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    KW - METIS-202028

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