Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Propagation of transition fronts in nonlinear chains with non-degenerate
  on-site potentials   We address the problem of a front propagation in chains with a bi-stable
nondegenerate on-site potential and a nonlinear gradient coupling. For a
generic nonlinear coupling, one encounters a special regime of transitions,
characterized by extremely narrow fronts, far supersonic velocities of
propagation and long waves in the oscillatory tail. This regime can be
qualitatively associated with a shock wave. The front propagation can be
described with the help of a simple reduced-order model; the latter delivers a
kinetic law, which is almost not sensitive to fine details of the on-site
potential. Besides, it is possible to predict all main characteristics of the
transition front, including its shape and frequency and amplitude of the
oscillatory tail. The numerical results are in a good agreement with the
analytical predictions. The suggested approach allows one to consider the
effects of an external pre-load and on-site damping. When the damping is
moderate, the analysis remains in the frame of the reduced-order model. It is
possible to consider the solution for the front propagating in the damped chain
as a perturbation of the undamped dynamics. This approach yield reasonable
predictions. When the damping is high, the transition front enters a completely
different asymptotic regime. The gradient nonlinearity generically turns
negligible, and the propagating front converges to the exact solution obtained
from a simple linear continuous model.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th