Solutions to Open WDVV Equations for the Universal Whitham Hierarchy

2025/12/03 by Ma, Shilin · 1 citation
#37K10 #53D45 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2512.03455

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 ℤ₂-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.

Citations

• Infinite-dimensional Frobenius Manifolds and Extensions of Genus-Zero Whitham Hierarchies
• Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies
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• On the Drinfeld-Sokolov Hierarchies of D type
• F-manifolds with flat structure and Dubrovin's duality
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Geometry of 2d topological field theories

Cited by

• Dubrovin duality for open Hurwitz flat F-manifolds

Related

• Open Saito theory for A and D singularities
• Infinite-dimensional Frobenius Manifolds Underlying the Universal Whitham Hierarchy
• Principal hierarchy of Frobenius manifolds with rational and trigonometric superpotentials
• Principal hierarchy of Infinite-dimensional Frobenius Manifold Underlying the Extended Kadomtsev-Petviashvili Hierarchy
• Real-normalized Whitham hierarchies and the WDVV equations