Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux--Egoroff equations. This system of partial differential equations appears as a specific subset of the $n$-component KP hierarchy. KP representation theory and the related Sato infinite Grassmannian are used to construct solutions of this Darboux--Egoroff system and the related Frobenius manifolds. Finally we show that for these solutions Dubrovin's isomonodromy tau-function can be expressed in the KP tau-function.
|Place of Publication||Enschede|
|Publisher||University of Twente, Department of Applied Mathematics|
|Publication status||Published - 1998|