Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-Parameter Method for Describing the Nonlinear Evolution of
  Narrow-Band Wave Trains   We consider the evolution of narrow-band wave trains of finite amplitude in a
nonlinear dispersive system which is described by the Klein--Gordon equation
with arbitrary polynomial nonlinearity. We use a new perturbative technique
which allows the original wave equation to be reduced to a model equation for
the wave train envelope (high-order nonlinear Schr\"{o}dinger equation). The
time derivative is expanded into an asymptotic series in two independent
parameters which characterize the smallness of amplitudes ($\varepsilon$) and
the slowness of their spatial variations ($\mu$). In contrast to other
perturbative methods in which these two parameters are taken equal (e.g., the
multiple scale method), the two-parameter method produces no secular terms. The
results of this study can be applied to investigating the propagation of
ultrashort (femtosecond) pulses in optical fibers, to studying the wave events
on a fluid surface, and to describing the Langmuir waves in hot plasmas.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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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: math
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg