Reciprocal transformations and flat metrics on Hurwitz spaces

Details Reciprocal transformations and flat metrics on Hurwitz spaces Reciprocal transformations and flat metrics on Hurwitz spaces

2007-04-13

arxiv.org/abs/0704.1779v2

J. Phys. A: Math. Theor. 40 (2007) 10769-10790

Nonlinear Sciences

Exactly Solvable and Integrable Systems

25 pages

Scientific paper

10.1088/1751-8113/40/35/004

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.

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