Geodesic
The~WDVV symmetries in two-primary models
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 367-381

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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.
Keywords: Frobenius manifold, WDVV equation, bi-Hamiltonian structure, primary free energy, dToda hierarchy, Benney hierarchy, dDym hierarchy, polytropic gas dynamics. 
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     author = {Yu-Tung Chen and Niann-Chern Lee and Ming-Hsien Tu},
     title = {The~WDVV symmetries in two-primary models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {161},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a5/}
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Yu-Tung Chen; Niann-Chern Lee; Ming-Hsien Tu. The~WDVV symmetries in two-primary models. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 367-381. http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a5/