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

Andrei Ya. Maltsev

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arXiv · solv-int/9910011

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

Andrei Ya. Maltsev

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Abstract

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

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Andrei Ya. Maltsev. 2017-07-27. The averaging of non-local Hamiltonian structures in Whitham's method. https://arxiv.org/abs/solv-int/9910011

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