Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of Gravity-Capillary Solitary Waves in Deep Water   The dynamics of solitary gravity-capillary water waves propagating on the
surface of a three-dimensional fluid domain is studied numerically. In order to
accurately compute complex time dependent solutions, we simplify the full
potential flow problem by taking a cubic truncation of the scaled
Dirichlet-to-Neumann operator for the normal velocity on the free surface. This
approximation agrees remarkably well with the full equations for the
bifurcation curves, wave profiles and the dynamics of solitary waves for a
two-dimensional fluid domain. Fully localised solitary waves are then computed
in the three-dimensional problem and the stability and interaction of both line
and localized solitary waves are investigated via numerical time integration of
the equations. The solitary wave branches are indexed by their finite energy at
small amplitude, and the dynamics of the solitary waves is complex involving
nonlinear focussing of wave packets, quasi-elastic collisions, and the
generation of propagating, spatially localised, time-periodic structures
(breathers).

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int