Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic
  limit, I   The nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the
nonrelativistic limit, namely as the speed of light $c$ tends to infinity, is
considered. In particular, a higher-order normalized approximation of NLKG
(which corresponds to the NLS at order $r=1$) is constructed, and when $M$ is a
smooth compact manifold or $\mathbb{R}^d$ it is proved that the solution of the
approximating equation approximates the solution of the NLKG locally uniformly
in time. When $M=\mathbb{R}^d$, $d \geq 3$, it is proved that solutions of the
linearized order $r$ normalized equation approximate solutions of linear
Klein-Gordon equation up to times of order $\mathcal{O}(c^{2(r-1)})$ for any
$r>1$.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys