Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the canonical forms of the multi-dimensional averaged Poisson
  brackets   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 canonical forms, which can be
obtained after transformations preserving the "physical meaning" of the field
variables. We show here that the averaged bracket can always be written in the
canonical form after a transformation of "Hydrodynamic Type" in the case of
absence of annihilators of initial bracket. However, in general case the
situation is more complicated. As we show here, in more general case the
averaged bracket can be transformed to a "pseudo-canonical" form under some
special ("physical") requirements on the initial bracket.

26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga