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Keldysh Institute preprints, 2012, 020, 28 pages (Mi ipmp38)  

This article is cited in 3 scientific papers (total in 3 papers)

Integrable Semidiscretization of Hyperbolic Equations – “Computational” Dispersion and Multidimensional Perspective

A. I. Aptekarev


Abstract: A goal of this preprint is to provide an analytical understanding of dispersive regularizations of hyperbolic shocks, in the context of completely integrable approximations to nonlinear hyperbolic Partial Differential Equations (PDEs) which exhibit shock formation. The fundamental analytical issue is to obtain a complete asymptotic description of continuum limits of integrable systems. Different families of completely integrable systems admit interpretation as semidiscrete approximations to hyperbolic PDEs – of these, the Toda lattice is a famous example. To investigate dispersive regularizations, it is required to carry out an asymptotic analysis of these systems in a very delicate continuum limit. Special attention will be paid to multidimensional (in space variables) generalizations.

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Citation: A. I. Aptekarev, “Integrable Semidiscretization of Hyperbolic Equations – “Computational” Dispersion and Multidimensional Perspective”, Keldysh Institute preprints, 2012, 020, 28 pp.

Citation in format AMSBIB
\Bibitem{Apt12}
\by A.~I.~Aptekarev
\paper Integrable Semidiscretization of Hyperbolic Equations -- ``Computational'' Dispersion and Multidimensional Perspective
\jour Keldysh Institute preprints
\yr 2012
\papernumber 020
\totalpages 28
\mathnet{http://mi.mathnet.ru/ipmp38}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Lapik, “Ekstremalnaya mera i vneshnee pole v dvuparametricheskikh vektornykh zadachakh ravnovesiya logarifmicheskogo potentsiala”, Preprinty IPM im. M. V. Keldysha, 2016, 115, 20 pp.  mathnet  crossref
    2. A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Samosopryazhennye matritsy Yakobi na grafakh i sovmestno ortogonalnye mnogochleny”, Preprinty IPM im. M. V. Keldysha, 2018, 003, 27 pp.  mathnet  crossref  elib
    3. A. I. Aptekarev, R. Kozhan, “Differential equations for the radial limits in $\mathbb{Z}_+^2$ of the solutions of a discrete integrable system”, Preprinty IPM im. M. V. Keldysha, 2018, 214, 20 pp.  mathnet  crossref
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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