Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integrable evolution equation for surface waves in deep water   In order to describe the dynamics of monochromatic surface waves in deep
water, we derive a nonlinear and dispersive system of equations for the free
surface elevation and the free surface velocity from the Euler equations in
infinite depth. From it, and using a multiscale perturbative methods, an
asymptotic model for small-aspect-ratio waves is derived. The model is shown to
be completely integrable. The Lax pair, the first conserved quantities as well
as the symmetries are exhibited. Theoretical and numerical studies reveal that
it supports periodic progressive Stokes waves which peak and break in finite
time. Comparison between the limiting wave solution of the asymptotic model and
classical irrotational results is performed.

1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph