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

G.F. Helminck, J.W. van de Leur, J.W. van de Leur

Research output: Book/ReportReportProfessional

### Abstract

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.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics 22 Published - 2002

### Publication series

Name Memorandum Faculty Mathematical Sciences University of Twente, Department of Applied Mathematics 1645 0169-2690

### Keywords

• METIS-208643
• MSC-22E65
• MSC-35Q58
• EWI-3465
• MSC-58B25
• IR-65831
• MSC-22E70

## Cite this

Helminck, G. F., van de Leur, J. W., & van de Leur, J. W. (2002). Elementary Darboux transformations for the $n$-component $KP$-hierarchy. (Memorandum Faculty Mathematical Sciences; No. 1645). Enschede: University of Twente, Department of Applied Mathematics.