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The averaging of nonlocal Hamiltonian structures in Whitham's method

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  • Andrei Ya. Maltsev

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.

Suggested Citation

  • Andrei Ya. Maltsev, 2002. "The averaging of nonlocal Hamiltonian structures in Whitham's method," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 30, pages 1-36, January.
    • Handle: RePEc:hin:jijmms:296321
    DOI: 10.1155/S0161171202106120
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