Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous derivation from the water waves equations of some full
  dispersion shallow water models   In order to improve the frequency dispersion effects of irrotational shallow
water models in coastal oceanography, several full dispersion versions of
classical models were formally derived in the literature. The idea, coming from
G. Whitham in [21], was to modify them so that their dispersion relation is the
same as the water waves equations. In this paper we construct new shallow water
approximations of the velocity potential then deducing ones on the vertically
averaged horizontal component of the velocity. We make use of them to derive
rigorously from the water waves equations two new Hamiltonian full dispersion
models. This provides for the first time non-trivial precision results
characterizing the order of approximation of the full dispersion models. They
are non-trivial in the sense that they are better than the ones for the
corresponding classical models.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol