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Reciprocal transformations and flat metrics on Hurwitz spaces

TitleReciprocal transformations and flat metrics on Hurwitz spaces
Publication TypeJournal Article
Year of Publication2007
AuthorsAbenda, S, Grava, T
JournalJ. Phys. A 40 (2007) 10769-10790
Abstract

We consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian structures. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltonian structure of Dubrovin-Novikov type. We show that, under our hypotheses, bi-hamiltonicity is preserved by the reciprocal transformation. Finally we apply such results to reciprocal systems of genus g Whitham-KdV modulation equations.

URLhttp://hdl.handle.net/1963/2210
DOI10.1088/1751-8113/40/35/004

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