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arxiv: hep-th/0104092 · v1 · pith:H4OYQU6Enew · submitted 2001-04-10 · ✦ hep-th · math-ph· math.AG· math.MP· nlin.SI

Solutions of the WDVV Equations and Integrable Hierarchies of KP type

classification ✦ hep-th math-phmath.AGmath.MPnlin.SI
keywords solutionsequationshierarchiesadditionalalgebracommutingconstructdarboux-egoroff
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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.

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