Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical solution of the small dispersion limit of Korteweg de Vries
  and Whitham equations   The Cauchy problem for the Korteweg de Vries (KdV) equation with small
dispersion of order $\epsilon^2$, is characterized by the appearance of a zone
of rapid modulated oscillations of wave-length of order $\epsilon$. These
oscillations are approximately described by the elliptic solution of KdV where
the amplitude, wave-number and frequency are not constant but evolve according
to the Whitham equations. In this manuscript we give a quantitative analysis of
the discrepancy between the numerical solution of the KdV equation in the small
dispersion limit and the corresponding approximate solution for values of
$\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are
compatible with a difference of order $\epsilon$ within the `interior' of the
Whitham oscillatory zone, of order $\epsilon^{1/3}$ at the left boundary
outside the Whitham zone and of order $\epsilon^{1/2}$ at the right boundary
outside the Whitham zone.

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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci