Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics near the threshold for blowup in the one-dimensional focusing
  nonlinear Klein-Gordon equation   We study dynamics near the threshold for blowup in the focusing nonlinear
Klein-Gordon equation $u_{tt}-u_{xx} + u - |u|^{2\alpha} u =0$ on the line.
Using mixed numerical and analytical methods we find that solutions starting
from even initial data, fine-tuned to the threshold, are trapped by the static
solution $S$ for intermediate times. The details of trapping are shown to
depend on the power $\alpha$, namely, we observe fast convergence to $S$ for
$\alpha>1$, slow convergence for $\alpha=1$, and very slow (if any) convergence
for $0<\alpha<1$. Our findings are complementary with respect to the recent
rigorous analysis of the same problem (for $\alpha>2$) by Krieger, Nakanishi,
and Schlag \cite{kns}.

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph