Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Camassa-Holm equation as the long-wave limit of the improved
  Boussinesq equation and of a class of nonlocal wave equations   In the present study we prove rigorously that in the long-wave limit, the
unidirectional solutions of a class of nonlocal wave equations to which the
improved Boussinesq equation belongs are well approximated by the solutions of
the Camassa-Holm equation over a long time scale. This general class of
nonlocal wave equations model bidirectional wave propagation in a nonlocally
and nonlinearly elastic medium whose constitutive equation is given by a
convolution integral. To justify the Camassa-Holm approximation we show that
approximation errors remain small over a long time interval. To be more
precise, we obtain error estimates in terms of two independent, small, positive
parameters $\epsilon$ and $\delta$ measuring the effect of nonlinearity and
dispersion, respectively. We further show that similar conclusions are also
valid for the lower order approximations: the Benjamin-Bona-Mahony
approximation and the Korteweg-de Vries approximation.

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph