Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instabilities in the two-dimensional cubic nonlinear Schrodinger
  equation   The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as
a model of phenomena in physical systems ranging from waves on deep water to
pulses in optical fibers. In this paper, we establish that every
one-dimensional traveling wave solution of NLS with trivial phase is unstable
with respect to some infinitesimal perturbation with two-dimensional structure.
If the coefficients of the linear dispersion terms have the same sign then the
only unstable perturbations have transverse wavelength longer than a
well-defined cut-off. If the coefficients of the linear dispersion terms have
opposite signs, then there is no such cut-off and as the wavelength decreases,
the maximum growth rate approaches a well-defined limit.

26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex