The multi-dimensional Hamiltonian structures in the Whitham method

@article{Maltsev2012TheMH,
  title={The multi-dimensional Hamiltonian structures in the Whitham method},
  author={Andrei Ya. Maltsev},
  journal={Journal of Mathematical Physics},
  year={2012},
  volume={54},
  pages={053507-053507}
}
  • A. Maltsev
  • Published 25 November 2012
  • Mathematics
  • Journal of Mathematical Physics
We consider the averaging of local field-theoretic Poisson brackets in the multi-dimensional case. As a result, we construct a local Poisson bracket for the regular Whitham system in the multidimensional situation. The procedure is based on the procedure of averaging of local conservation laws and follows the Dubrovin–Novikov scheme of the bracket averaging suggested in one-dimensional case. However, the features of the phase space of modulated parameters in higher dimensions lead to a… 

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