Solutions of the WDVV Equations and Integrable Hierarchies of KP type

Abstract

We show that reductions of KP hierarchies related to the loop algebra of $S{L}_n$ with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to include a set of commuting additional symmetries, we construct solutions of the Witten--Dijkgraaf--E. Verlinde--H. Verlinde equations.

28 pages, LaTeX

References in corpus (2)

• Integrable Hierarchy for Multidimensional Toda Equations and Topological-Anti-topological Fusion
• Twisted GL_n Loop Group Orbit and Solutions of the WDVV Equations

Cited by in corpus (5)

• Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations
• Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach
• WDVV Equations, Darboux-Egoroff Metric and the Dressing Method
• On construction of symmetries and recursion operators from zero-curvature representations and the Darboux-Egoroff system
• Integrable Structure behind WDVV Equations