Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonances in the dynamics of $\phi^4$ kinks perturbed by ac forces   We study the dynamics of $\phi^4$ kinks perturbed by an ac force, both with
and without damping. We address this issue by using a collective coordinate
theory, which allows us to reduce the problem to the dynamics of the kink
center and width. We carry out a careful analysis of the corresponding ordinary
differential equations, of Mathieu type in the undamped case, finding and
characterizing the resonant frequencies and the regions of existence of
resonant solutions. We verify the accuracy of our predictions by numerical
simulation of the full partial differential equation, showing that the
collective coordinate prediction is very accurate. Numerical simulations for
the damped case establish that the strongest resonance is the one at half the
frequency of the internal mode of the kink. In the conclusion we discuss on the
possible relevance of our results for other systems, especially the sine-Gordon
equation. We also obtain additional results regarding the equivalence between
different collective coordinate methods applied to this problem.

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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an