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Solutions of the WDVV Equations and Integrable Hierarchies of KP type

We show that reductions of KP hierarchies related to the loop algebra of $SL_n$ 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.

preprint2001arXivOpen access
H. AratynJ. van de Leur
math-phmath.MPmath.AGnlin.SIhep-th
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H. AratynJ. van de Leur

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