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International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 7, Pages 399-434
http://dx.doi.org/10.1155/S0161171202106120

The averaging of nonlocal Hamiltonian structures in Whitham's method

1Landau Institute for Theoretical Physics, 117940, Kosygina 2, Moscow, Russia
2SISSA-ISAS, Via Beirut 2-4, Trieste 34014, Italy

Received 16 June 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the m-phase Whitham's averaging method and propose the procedure of “averaging” nonlocal Hamiltonian structures. The procedure is based on the existence of a sufficient number of local-commuting integrals of the system and gives the Poisson bracket of Ferapontov type for Whitham's system. The method can be considered as the generalization of the Dubrovin-Novikov procedure for the local field-theoretical brackets.