# $\tau$-Functions for a two-point version of the $KP$-hierarchy

G.F. Helminck

Research output: Book/ReportReportProfessional

### Abstract

In this paper a multipoint version of the linearization of the $KP$-hierarchy is described. Solutions of this system in the form of wave functions are constructed starting from a suitable Grassmann manifold and a group of commuting flows corresponding to the configuration of $n$ points in $\mathbb{C}$. The failure of equivariance at lifting these flows to the determinant bundle over this Grassmann manifold is measured by the determinants of certain Fredholm operators, the so-called $\tau$-functions. In the case of two points an explicit relation between these $\tau$-functions and the wave functions is derived.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics 15 Published - 2003

### Publication series

Name Memorandum University of Twente, Department of Applied Mathematics 1671 0169-2690

### Keywords

• MSC-35Q53
• MSC-35Q58
• MSC-22E65
• METIS-211955
• MSC-58B25
• IR-65856
• EWI-3491
• MSC-22E70

## Cite this

Helminck, G. F. (2003). $\tau$-Functions for a two-point version of the $KP$-hierarchy. (Memorandum; No. 1671). Enschede: University of Twente, Department of Applied Mathematics.