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arXiv · 2512.03455

Solutions to Open WDVV Equations for the Universal Whitham Hierarchy

Shilin Ma
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Abstract

In this paper, we construct a pair of solutions to the open WDVV equations associated with the infinite-dimensional Frobenius manifolds that underlie the genus-zero universal Whitham hierarchy, and for the resulting flat F-manifolds, we explicitly construct their principal hierarchies. We further demonstrate that this construction is compatible with finite-dimensional reductions, yielding solutions for Frobenius manifolds associated with general rational superpotentials and those subject to a $\mathbb{Z}_{2}$-symmetry reduction. In particular, the polynomial solutions derived by Basalaev and Buryak via open Saito theory for A- and D-type singularities are recovered as special cases.

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Shilin Ma. 2025-12-03. Solutions to Open WDVV Equations for the Universal Whitham Hierarchy. https://arxiv.org/abs/2512.03455

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