### Abstract

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

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 16 |

Publication status | Published - 2004 |

### Publication series

Name | Memorandum |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1744 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-22E70
- MSC-58B25
- IR-65928
- MSC-35Q58
- MSC-22E65
- METIS-227110
- EWI-3564

### Cite this

*Spaces of boundary values related to a multipoint version of the KP-hierarchy*. (Memorandum; No. 1744). Enschede: University of Twente, Department of Applied Mathematics.

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*Spaces of boundary values related to a multipoint version of the KP-hierarchy*. Memorandum, no. 1744, University of Twente, Department of Applied Mathematics, Enschede.

**Spaces of boundary values related to a multipoint version of the KP-hierarchy.** / Helminck, G.F.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Spaces of boundary values related to a multipoint version of the KP-hierarchy

AU - Helminck, G.F.

N1 - Imported from MEMORANDA

PY - 2004

Y1 - 2004

N2 - In this paper one considers a finite number of points in the complex plane and various spaces of boundary values on circles surrounding these points. To this geometric configuration one associates a Grassmann manifolds that is shown to yield solutions of a multipoint version of the linearization of the $KP$-hierarchy. These Grassmann manifolds are built in such a way that the determinant line bundle and its dual over them still make sense. The same holds for the so-called $\tau$-functions, determinants of certain Fredholm operators that measure the failure of equivariance at lifting the commuting flows of ths hierarchy to these bundles. Solutions of the linearization are described by wave functions of a certain type. They are perturbations of the trivial solution with the leading term of the perturbation determining the type. One concludes with showing that, if a plane in the Grassmann manifold yields wave functions of different types, they are connected by a differential operator in the coordinates of the flows.

AB - In this paper one considers a finite number of points in the complex plane and various spaces of boundary values on circles surrounding these points. To this geometric configuration one associates a Grassmann manifolds that is shown to yield solutions of a multipoint version of the linearization of the $KP$-hierarchy. These Grassmann manifolds are built in such a way that the determinant line bundle and its dual over them still make sense. The same holds for the so-called $\tau$-functions, determinants of certain Fredholm operators that measure the failure of equivariance at lifting the commuting flows of ths hierarchy to these bundles. Solutions of the linearization are described by wave functions of a certain type. They are perturbations of the trivial solution with the leading term of the perturbation determining the type. One concludes with showing that, if a plane in the Grassmann manifold yields wave functions of different types, they are connected by a differential operator in the coordinates of the flows.

KW - MSC-22E70

KW - MSC-58B25

KW - IR-65928

KW - MSC-35Q58

KW - MSC-22E65

KW - METIS-227110

KW - EWI-3564

M3 - Report

T3 - Memorandum

BT - Spaces of boundary values related to a multipoint version of the KP-hierarchy

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -