### 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 language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 33 |

Publication status | Published - 2000 |

### Publication series

Name | Memorandum Faculteit TW |
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Publisher | University 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.