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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 1, Pages 42–54 (Mi ufa370)  

This article is cited in 1 scientific paper (total in 1 paper)

Modelling compression waves with a large initial gradient in the Korteweg–de Vries hydrodynamics

S. V. Zakharov, A. E. Elbert

N. N. Krasovskii Institute of Mathematics and Mechanics, S. Kovalevskaya str., 16, 620990, Ekaterinburg, Russia

Abstract: We consider the Cauchy problem for the Korteweg–de Vries equation with a small parameter at the higher derivative and a large gradient of the initial function. By means of the numerical and analytic methods we show that the formal asymptotics obtained by renormalization is an asymptotic solution to the KdV equation. We obtain the graphs of the asymptotic solutions including the case of non-monotone initial data.

Keywords: Korteweg–de Vries equation, Cauchy problem, compression wave.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The work is supported by the complex program of fundamental scientific researches of UB RAS (project “Developing of new analytic, numeric and asymptotic methods for studying problems of mathematical physics and their applications to signal processing”.


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English version:
Ufa Mathematical Journal, 2017, 9:1, 41–53 (PDF, 252 kB); https://doi.org/10.13108/2017-9-1-41

Bibliographic databases:

UDC: 517.958
MSC: 35Q53
Received: 04.12.2015

Citation: S. V. Zakharov, A. E. Elbert, “Modelling compression waves with a large initial gradient in the Korteweg–de Vries hydrodynamics”, Ufimsk. Mat. Zh., 9:1 (2017), 42–54; Ufa Math. J., 9:1 (2017), 41–53

Citation in format AMSBIB
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\paper Modelling compression waves with a~large initial gradient in the Korteweg--de~Vries hydrodynamics
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\vol 9
\issue 1
\pages 42--54
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\pages 41--53
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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. 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
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