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TMF, 2013, Volume 175, Number 2, Pages 173–177 (Mi tmf8437)  

This article is cited in 2 scientific papers (total in 2 papers)

Renormalization in the Cauchy problem for the Korteweg–de Vries equation

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Division, RAS, Yekaterinburg, Russia

Abstract: We consider the Cauchy problem for the Korteweg–de Vries equation with a small parameter at the highest derivative and a large gradient of the initial function. We construct an asymptotic solution of this problem by the renormalization method.

Keywords: Korteweg–de Vries equation, Cauchy problem, asymptotic solution, renormalization

DOI: https://doi.org/10.4213/tmf8437

Full text: PDF file (280 kB)
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English version:
Theoretical and Mathematical Physics, 2013, 175:2, 592–595

Bibliographic databases:

Received: 29.10.2012

Citation: S. V. Zakharov, “Renormalization in the Cauchy problem for the Korteweg–de Vries equation”, TMF, 175:2 (2013), 173–177; Theoret. and Math. Phys., 175:2 (2013), 592–595

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf8437
  • https://doi.org/10.4213/tmf8437
  • http://mi.mathnet.ru/eng/tmf/v175/i2/p173

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Zakharov, A. E. Elbert, “Modelling compression waves with a large initial gradient in the Korteweg–de Vries hydrodynamics”, Ufa Math. J., 9:1 (2017), 41–53  mathnet  crossref  isi  elib
    2. Alexander E. Elbert, Sergey V. Zakharov, “Dispersive rarefaction wave with a large initial gradient”, Ural Math. J., 3:1 (2017), 33–43  mathnet  crossref  mathscinet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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