Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical dynamics and coherent soliton condensates in self-focusing
  nonlinear media with periodic initial conditions   The small dispersion limit of the focusing nonlinear Schrodinger equation
with periodic initial conditions is studied analytically and numerically.
First, through a comprehensive set of numerical simulations, it is demonstrated
that solutions arising from a certain class of initial conditions, referred to
as "periodic single-lobe" potentials, share the same qualitative features,
which also coincide with those of solutions arising from localized initial
conditions. The spectrum of the associated scattering problem in each of these
cases is then numerically computed, and it is shown that such spectrum is
confined to the real and imaginary axes of the spectral variable in the
semiclassical limit. This implies that all nonlinear excitations emerging from
the input have zero velocity, and form a coherent nonlinear condensate.
Finally, by employing a formal Wentzel-Kramers-Brillouin expansion for the
scattering eigenfunctions, asymptotic expressions for the number and location
of the bands and gaps in the spectrum are obtained, as well as corresponding
expressions for the relative band widths and the number of "effective
solitons". These results are shown to be in excellent agreement with those from
direct numerical computation of the eigenfunctions. In particular, a scaling
law is obtained showing that the number of effective solitons is inversely
proportional to the small dispersion parameter.

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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg