Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A necessary and sufficient condition on scattering for the regularly
  hyperbolic systems   The present paper is devoted to finding a necessary and sufficient condition
on the occurence of scattering for the regularly hyperbolic systems with
time-dependent coefficients whose time-derivatives are integrable over the real
line. More precisely, it will be shown that the solutions are asymptotically
free if the coefficients are stable in the sense of the Riemann integrability
as time goes to infinity, while each nontrivial solution is never
asymptotically free provided that the coefficients are not R-stable as times
goes to infinity. As a by-product, the scattering operator can be constructed.
It is expected that the results obtained in the present paper would be brought
into the study of the asymptotic behaviour of Kirchhoff systems.

32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn