Solutions to Open WDVV Equations for the Universal Whitham Hierarchy

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.