Legendre transforms for type An and Bn -systems
Abstract
The Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations have a rich structure related to the theory of Frobenius manifolds, with many known families of solutions. A Legendre transformation is a symmetry of the WDVV equations, introduced by Dubrovin. We explicitly compute the results of a Legendre transformation applied to An- and Bn-type multi-parameter rational solutions, relating them to known and new trigonometric solutions.
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