Ufa Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Ufa Mathematical Journal, 2017, Volume 9, Issue 1, Pages 41–53
DOI: https://doi.org/10.13108/2017-9-1-41 (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
English version PDF (252 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.13108/2017-9-1-41
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”.
Received: 04.12.2015
Russian version:
Ufimskii Matematicheskii Zhurnal, 2017, Volume 9, Issue 1, Pages 42–54
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35Q53
Language: English
Original paper language: Russian
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
\Bibitem{ZakElb17}
\by S.~V.~Zakharov, A.~E.~Elbert
\paper Modelling compression waves with a~large initial gradient in the Korteweg--de~Vries hydrodynamics
\jour Ufimsk. Mat. Zh.
\yr 2017
\vol 9
\issue 1
\pages 42--54
\mathnet{http://mi.mathnet.ru/ufa370}
\elib{https://elibrary.ru/item.asp?id=29009894}
\transl
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 1
\pages 41--53
\crossref{https://doi.org/10.13108/2017-9-1-41}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000411736500004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018744341}
Linking options:
  • https://www.mathnet.ru/eng/ufa370
  • https://doi.org/10.13108/2017-9-1-41
  • https://www.mathnet.ru/eng/ufa/v9/i1/p42
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Уфимский математический журнал
    Statistics & downloads:
    Abstract page:236
    Russian version PDF:89
    English version PDF:9
    References:41
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024