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

The averaging of nonlocal Hamiltonian structures in Whitham's method

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.