On Symmetries of the WDVV Equations

2010/01/30 by Dingdian Xu, Youjin Zhang, Xu, Dingdian +1
Chemistry · Mathematics · Physics and Astronomy · #35Q53 #53Z05 #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1002.0034

openalex publication_date 2010/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For two solutions of the WDVV equations that are related by two types of symmetries of the equations given by Dubrovin, we show that the associated principal hierarchies of integrable systems are related by certain reciprocal transformation, and the tau functions of the hierarchies are either identical or related by a Legendre transformation. We also consider relationships between the Virasoro constraints and topological deformations of the principal hierarchies.

Citations

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Extended affine Weyl groups and Frobenius manifolds

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