Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time asymptotics of the one-dimensional damped nonlinear
  Klein-Gordon equation   For the one-dimensional nonlinear damped Klein-Gordon equation \[
\partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad
\mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove
that any global finite energy solution either converges to $0$ or behaves
asymptotically as $t\to \infty$ as the sum of $K\geq 1$ decoupled solitary
waves. In the multi-soliton case $K\geq 2$, the solitary waves have alternate
signs and their distances are of order $\log t$.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph