# 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} }

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…

## 4 Citations

### On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations

- Mathematics
- 2015

We consider the questions connected with the Hamiltonian properties of the Whitham equations in case of several spatial dimensions. An essential point of our approach here is a connection of the…

### On the canonical forms of the multi-dimensional averaged Poisson brackets

- Mathematics, Physics
- 2015

We consider here special Poisson brackets given by the "averaging" of local multi-dimensional Poisson brackets in the Whitham method. For the brackets of this kind it is natural to ask about their…

### The averaging of multi-dimensional Poisson brackets for systems having pseudo-phases

- Mathematics
- 2014

We consider features of the Hamiltonian formulation of the Whitham method in the presence of pseudo-phases. As we show, an analog of the procedure of averaging of the Poisson bracket with the reduced…

### Gerald Beresford Whitham. 13 December 1927 — 26 January 2014

- MathematicsBiographical Memoirs of Fellows of the Royal Society
- 2015

Gerald Beresford Whitham was one of the leading applied mathematicians of the twentieth century. His original, deep and insightful research into nonlinear wave propagation formed the foundation of…

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