The averaging of non-local Hamiltonian structures in Whitham's method

Details The averaging of non-local Hamiltonian structures in Whitham's method The averaging of non-local Hamiltonian structures in Whitham's method

1999-10-28

arxiv.org/abs/solv-int/9910011v6

Intern. Journ. of Math. and Math. Sci. 30:7 (2002) 399-434

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Latex, 50 Pages

Scientific paper

We consider the $m$-phase Whitham's averaging method and propose the procedure of "averaging" of non-local 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.

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