Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the decoupling of the improved Boussinesq equation into two uncoupled
  Camassa-Holm equations   We rigorously establish that, in the long-wave regime characterized by the
assumptions of long wavelength and small amplitude, bidirectional solutions of
the improved Boussinesq equation tend to associated solutions of two uncoupled
Camassa-Holm equations. We give a precise estimate for approximation errors in
terms of two small positive parameters measuring the effects of nonlinearity
and dispersion. Our results demonstrate that, in the present regime, any
solution of the improved Boussinesq equation is split into two waves
propagating in opposite directions independently, each of which is governed by
the Camassa-Holm equation. We observe that the approximation error for the
decoupled problem considered in the present study is greater than the
approximation error for the unidirectional problem characterized by a single
Camassa-Holm equation. We also consider lower order approximations and we state
similar error estimates for both the Benjamin-Bona-Mahony approximation and the
Korteweg-de Vries approximation.

37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph