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TMF, 2008, Volume 154, Number 2, Pages 294–304 (Mi tmf6170)  

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

Korteweg–de Vries hierarchy as an asymptotic limit of the Boussinesq system

S. A. Kordyukova

Ufa State Aviation Technical University

Abstract: For the model of surface waves, we perform an asymptotic analysis with respect to a small parameter $\varepsilon$ for large times where corrections to the approximation described by the Korteweg–de Vries equation must be taken into account. We reveal the appearance of the Korteweg–de Vries hierarchy, which ensures the construction of an asymptotic representation up to the times $t\approx\varepsilon^{-2}$, where the Korteweg–de Vries approximation becomes inapplicable.

Keywords: nonlinear equation, small parameter, potentiated Korteweg–de Vries equation, Lie–Bäcklund canonical operator, multiscale method, asymptotic representation, soliton

DOI: https://doi.org/10.4213/tmf6170

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English version:
Theoretical and Mathematical Physics, 2008, 154:2, 250–259

Bibliographic databases:

Received: 06.03.2007

Citation: S. A. Kordyukova, “Korteweg–de Vries hierarchy as an asymptotic limit of the Boussinesq system”, TMF, 154:2 (2008), 294–304; Theoret. and Math. Phys., 154:2 (2008), 250–259

Citation in format AMSBIB
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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. Helal M.A. Seadawy A.R. Zekry M.H., “Stability Analysis of Solitary Wave Solutions For the Fourth-Order Nonlinear Boussinesq Water Wave Equation”, Appl. Math. Comput., 232 (2014), 1094–1103  crossref  mathscinet  zmath  isi  scopus
    2. Helal M.A. Seadawy A.R. Zekry M., “Stability Analysis of Solutions For the Sixth-Order Nonlinear Boussinesq Water Wave Equations in Two-Dimensions and Its Applications”, Chin. J. Phys., 55:2 (2017), 378–385  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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