The construction of Frobenius manifolds from KP tau-functions

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.

29 pages, latex2e, no figures

Cited by in corpus (7)

• Kontsevich-Witten Model From 2+1 Gravity: New Exact Combinatorial Solution
• Givental symmetries of Frobenius manifolds and multi-component KP tau-functions
• Solutions of the WDVV Equations and Integrable Hierarchies of KP type
• Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach
• Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows
• On construction of symmetries and recursion operators from zero-curvature representations and the Darboux-Egoroff system
• Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation