Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of quasipattern solutions of the Swift-Hohenberg
  equation   Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial
direction) remain one of the outstanding problems of pattern formation. As with
problems involving quasiperiodicity, there is a small divisor problem. In this
paper, we consider 8-fold, 10-fold, 12-fold, and higher order quasipattern
solutions of the Swift-Hohenberg equation. We prove that a formal solution,
given by a divergent series, may be used to build a smooth quasiperiodic
function which is an approximate solution of the pattern-forming PDE up to an
exponentially small error.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph