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The construction of Frobenius manifolds from KP tau-functions

J. W. van de Leur·R. Martini
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Abstract

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.

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BibTeXRIS

J. W. van de Leur, R. Martini. 1998-08-18. The construction of Frobenius manifolds from KP tau-functions. https://doi.org/10.1007/s002200050691

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