Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian Dysthe equation for 3D deep-water gravity waves   This article concerns the water wave problem in a three-dimensional domain of
infinite depth and examines the modulational regime for weakly nonlinear
wavetrains. We use the method of normal form transformations near the
equilibrium state to provide a new derivation of the Hamiltonian Dysthe
equation describing the slow evolution of the wave envelope. A precise
calculation of the third-order normal form allows for a refined reconstruction
of the free surface. We test our approximation against direct numerical
simulations of the three-dimensional Euler system and against predictions from
the classical Dysthe equation, and find very good agreement.

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The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci