Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Whitham equations and phase shifts for the Korteweg-deVries equation   The semi-classical Korteweg-deVries equation for step-like data is considered
with a small parameter in front of the highest derivative. Using perturbation
analysis Whitham theory is constructed to higher order. This allows the order
one phase and the complete leading order solution to be obtained; the results
are confirmed by extensive numerical calculations.

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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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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: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol