Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solitary waves in one-dimensional pre-stressed lattice and its continual
  analog   One of the most interesting phenomena occuring in nonlinear media models is
the existence of wave patterns, such as kinks, solitons, compactons, peakons
and many others. There are known numerous nonlinear evolutionary PDEs,
supporting soliton (multi-soliton) and compacton traveling wave (TW) solutions.
Unfortunately, the vast majority of the models, with the exception of
completely integrable ones, do not enable to analyze the properties of solitary
waves interaction using only qualitative methods. Therefore it is instructive,
when dealing with the non-integrable PDEs, to combine the qualitative treatment
with numerical simulations. In this report we are going to present the results
of studying compacton solutions in the continual models for granular
pre-stressed chains. The model is shown to possess a pair of compacton TW
solutions which are the bright and dark compactons. First we consider the
stability properties of the compacton solutions and show that both the bright
and the dark compactons pass the stability test. Next we analyze the dynamics
of the compactons, simulating numerically the temporal evolution of a single
compacton, a well as the interection of pairs of compactons, including
bright-bright, dark-dark and bright-dark pairs. To be able to simulate the
evolutin of interacting compactons, we have modified the numerical scheme built
by J. de Frutos, M. A. Lopez-Marcos, and J. M. Sanz-Serna. Results of
simulations are compared with that of evolution of corresponding impulse in the
granular pre-stressed chain.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: stat
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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: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: math