Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq
  equation   In this paper, we develop computer-assisted techniques for the analysis of
periodic orbits of ill-posed partial differential equations. As a case study,
our proposed method is applied to the Boussinesq equation, which has been
investigated extensively because of its role in the theory of shallow water
waves. The idea is to use the symmetry of the solutions and a
Newton-Kantorovich type argument (the radii polynomial approach), to obtain
rigorous proofs of existence of the periodic orbits in a weighted $\ell^1$
Banach space of space-time Fourier coefficients with geometric decay. We
present several computer-assisted proofs of existence of periodic orbits at
different parameter values.

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The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph