Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: KAM for the nonlinear wave equation on the circle: small amplitude
  solution
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol