Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time existence and resonant approximation for the quadratic
  nonlinear wave equation with an anisotropic harmonic trapping   We establish long-time existence and uniqueness for the 2D wave equation with
a harmonic potential in one direction. This proof relies on a fine study of the
so-called space-time resonances of the equation. Then we derive a resonant
system for this equation and we prove that it is a satisfying approximation for
the original equation.

5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom