Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical study of the stability of the Peregrine breather   The Peregrine breather is widely discussed as a model for rogue waves in deep
water. We present here a detailed numerical study of perturbations of the
Peregrine breather as a solution to the nonlinear Schr\"odinger (NLS)
equations. We first address the modulational instability of the constant
modulus solution to NLS. Then we study numerically localized and nonlocalized
perturbations of the Peregrine breather in the linear and fully nonlinear
setting. It is shown that the solution is unstable against all considered
perturbations.

29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph