### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 22 |

Publication status | Published - 2002 |

### Publication series

Name | Memorandum Faculty Mathematical Sciences |
---|---|

Publisher | University 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

*Elementary Darboux transformations for the $n$-component $KP$-hierarchy*. (Memorandum Faculty Mathematical Sciences; No. 1645). Enschede: University of Twente, Department of Applied Mathematics.

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*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.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Elementary Darboux transformations for the $n$-component $KP$-hierarchy

AU - Helminck, G.F.

AU - van de Leur, J.W.

AU - van de Leur, J.W.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

N2 - 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.

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

KW - MSC-35Q58

KW - EWI-3465

KW - MSC-58B25

KW - IR-65831

KW - MSC-22E70

M3 - Report

T3 - Memorandum Faculty Mathematical Sciences

BT - Elementary Darboux transformations for the $n$-component $KP$-hierarchy

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -