Abstract

From the bi-Hamiltonian standpoint, we investigate symmetries of Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations proposed by Dubrovin. These symmetries can be viewed as canonical Miura transformations between genus-zero bi-Hamiltonian systems of hydrodynamic type. In particular, we show that the moduli space of two-primary models under symmetries of the WDVV equations can be parameterized by the polytropic exponent h. We discuss the transformation properties of the free energy at the genus-one level.

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