Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Laguerre polynomials and transitional asymptotics of the modified
  Korteweg-de Vries equation for step-like initial data   We consider the compressive wave for the modified Korteweg--de Vries equation
with background constants $c>0$ for $x\to-\infty$ and $0$ for $x\to+\infty.$ We
study the asymptotics of solutions in the transition zone $4c^2t-\varepsilon
t<x<4c^2t-\beta t^{\sigma}\ln t$ for $\varepsilon>0,$ $\sigma\in(0,1),$
$\beta>0.$ In this region we have a bulk of nonvanishing oscillations, the
number of which grows as $\frac{\varepsilon t}{\ln t}.$ Also we show how to
obtain Khruslov--Kotlyarov's asymptotics in the domain $4c^2t-\rho\ln
t<x<4c^2t$ with the help of parametrices constructed out of Laguerre
polynomials in the corresponding Riemann-Hilbert problem.

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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: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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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: econ
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat