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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 3, Pages 459–472 (Mi zvmmf10696)  

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

Compactons and Riemann waves of an extended modified Korteweg–de Vries equation with nonlinear dispersion

S. P. Popov

Dorodnicyn Computing Center, Federal Research Center УComputer Science and ControlФ, Russian Academy of Sciences, Moscow, Russia

Abstract: The $\mathrm{K}(f^m, g^n)$ equation is studied, which generalizes the modified Korteweg–de Vries equation $\mathrm{K}(u^3, u^1)$ and the Rosenau–Hyman equation $\mathrm{K}(u^m, u^n)$ to other dependences of nonlinearity and dispersion on the solution. The considered functions $f(u)$ and $g(u)$ can be linear or can have the form of a smoothed step. It is found numerically that, depending on the form of nonlinearity and dispersion, the given equation has compacton and kovaton solutions, Riemann-wave solutions, and oscillating wave packets of two types. It is shown that the interaction between solutions of all found types occurs with the preservation of their parameters.

Key words: KdV equation, mKdV equation, $\mathrm{K}(m, n)$ equation, Rosenau–Hyman equation, $\mathrm{K}(\cos)$ equation, the Rosenau–Pikovsky equation, compacton, kovaton, soliton, kink, Riemann wave, oscillatory waves, wave packets, multisoliton interaction.

DOI: https://doi.org/10.7868/S0044466918030122

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:3, 437–448

Bibliographic databases:

UDC: 519.634
Received: 19.10.2016
Revised: 13.03.2017

Citation: S. P. Popov, “Compactons and Riemann waves of an extended modified Korteweg–de Vries equation with nonlinear dispersion”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 459–472; Comput. Math. Math. Phys., 58:3 (2018), 437–448

Citation in format AMSBIB
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\paper Compactons and Riemann waves of an extended modified Korteweg--de Vries equation with nonlinear dispersion
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 3
\pages 459--472
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\crossref{https://doi.org/10.7868/S0044466918030122}
\elib{https://elibrary.ru/item.asp?id=32615748}
\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 3
\pages 437--448
\crossref{https://doi.org/10.1134/S0965542518030107}
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    This publication is cited in the following articles:
    1. Gumerov A.M., Ekomasov E.G., Kudryavtsev V R., Fakhretdinov I M., “Localized Magnetic Inhomogeneities Generation on Defects as a New Channel of Damping For a Moving Domain Wall”, Lett. Mater., 8:3 (2018), 299–304  crossref  isi
    2. A. M. Gumerov, E. G. Ekomasov, R. V. Kudryavtsev, M. I. Fakhretdinov, “Excitation of Large-Amplitude Localized Nonlinear Waves by the Interaction of Kinks of the Sine-Gordon Equation with Attracting Impurity”, Rus. J. Nonlin. Dyn., 15:1 (2019), 21–34  mathnet  crossref  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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