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arXiv · 0911.0607

The conservation of the Hamiltonian structures in the deformations of the Whitham systems

A. Ya. Maltsev
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Abstract

We consider the construction of the deformed Whitham system for the KdV-equation in the one-phase case and investigate the conservation of the Hamiltonian properties in this situation. It is shown then, that both the Gardner - Zakharov - Faddeev and the Magri brackets give the deformed Dubrovin - Novikov brackets (the brackets of Dubrovin - Zhang type) for the deformed Whitham system constructed by our procedure. The general approach used in the paper gives a scheme for the averaging of the Poisson structures in the general situation.

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A. Ya. Maltsev. 2009-11-03. The conservation of the Hamiltonian structures in the deformations of the Whitham systems. https://doi.org/10.1088/1751-8113/43/6/065202

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