Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Length-scale competition in the damped sine-Gordon chain   It is shown that there are two different regimes for the damped sine-Gordon
chain driven by the spatio-temporal periodic force $\Gamma sin(\omega t - k_{n}
x)$ with a flat initial condition. For $\Gamma_{c}(n)$ to a translating {\em
2-breather} excitation from a state locked to the driver. For $\omega < k_{n}$,
the excitations of the system are the locked states with the phase velocity
$\omega/k_{n}$ in all the region of $\Gamma$ studied. In the first regime, the
frequency of the breathers is controlled by $\omega$, and the velocity of the
breathers, controlled by $k_{n}$, is shown to be the group velocity determined
from the linear dispersion relation for the sine-Gordon equation. A linear
stability analysis reveals that, in addition to two competing length-scales,
namely, the width of the breathers and the spatial period of the driving, there
is one more length-scale which plays an important role in controlling the
dynamics of the system at small driving. In the second regime the length-scale
$k_{n}$ controls the excitation. The above picture is further corroborated by
numerical nonlinear spectral analysis. An energy balance estimate is also
presented and shown to predict the critical value of $\Gamma$ in good agreement
with the numerics.

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The categories of this paper are: hep-th
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn