Geometric Bäcklund-Darboux transformations for the KP-hierarchy

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

doi:10.2977/prims/1145477327

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 journal › Article › Academic › peer-review

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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 language	Undefined
Pages (from-to)	479-519
Journal	Research institute for mathematical sciences. Publications
Volume	37
Issue number	4
DOIs	https://doi.org/10.2977/prims/1145477327
Publication status	Published - 2001

Keywords

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

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10.2977/prims/1145477327

Helminck01geometric

Cite this

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title = "Geometric B{\"a}cklund-Darboux transformations for the KP-hierarchy",

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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AU - van de Leur, J.W.

AU - van de Leur, Johan W.

N1 - Open Access

PY - 2001

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AB - 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.

KW - Toda lattice hierarchy

KW - KP hierarchy

KW - IR-70361

KW - Bäcklund-Darboux transformation

KW - METIS-202028

KW - Constrained KP

KW - Grassmann manifold

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