International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 7, Pages 399-434
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 Andrei Ya. Maltsev. 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.
We consider the -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.