We consider hydrodynamic systems which possess a local Hamiltonian structure. 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. 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.
Reciprocal transformations and flat metrics on Hurwitz spaces / S. Abenda; T. Grava. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - STAMPA. - 40:(2007), pp. 10769-10790. [10.1088/1751-8113/40/35/004]
Reciprocal transformations and flat metrics on Hurwitz spaces
ABENDA, SIMONETTA;
2007
Abstract
We consider hydrodynamic systems which possess a local Hamiltonian structure. 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. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.