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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 3, Pages 515–528 (Mi zvmmf8088)  

This article is cited in 5 scientific papers (total in 5 papers)

Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations

I. B. Bakholdina, E. R. Egorovab

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia
b Yakut State University, ul. Belinskogo 58, Yakutsk, 677000 Russia

Abstract: Electron magnetohydrodynamics equations are derived with allowance for nonlinearity, dispersion, and dissipation caused by friction between the ions and electrons. These equations are transformed into a form convenient for the construction of a numerical scheme. The interaction of codirectional and oppositely directed magnetosonic solitary waves with no dissipation is computed. In the first case, the solitary waves are found to behave as solitons (i.e., their amplitudes after the interaction remain the same), while, in the second case, waves are emitted that lead to decreased amplitudes. The decay of a solitary wave due to dissipation is computed. In the case of weak dissipation, the solution is similar to that of the Riemann problem with a structure combining a discontinuity and a solitary wave. The decay of a solitary wave due to dispersion is also computed, in which case the solution can also be interpreted as one with a discontinuity. The decay of a solitary wave caused by the combined effect of dissipation and dispersion is analyzed.

Key words: plasma, electron MHD, solitary waves, dispersion, nonlinearity, dissipation.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:3, 477–489

Bibliographic databases:

UDC: 519.634
Received: 02.06.2010
Revised: 10.09.2010

Citation: I. B. Bakholdin, E. R. Egorova, “Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations”, Zh. Vychisl. Mat. Mat. Fiz., 51:3 (2011), 515–528; Comput. Math. Math. Phys., 51:3 (2011), 477–489

Citation in format AMSBIB
\by I.~B.~Bakholdin, E.~R.~Egorova
\paper Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2011
\vol 51
\issue 3
\pages 515--528
\jour Comput. Math. Math. Phys.
\yr 2011
\vol 51
\issue 3
\pages 477--489

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    This publication is cited in the following articles:
    1. I. B. Bakholdin, “Metody issledovaniya, teoriya i klassifikatsiya obratimykh struktur razryvov v modelyakh gidrodinamicheskogo tipa”, Preprinty IPM im. M. V. Keldysha, 2013, 030, 40 pp.  mathnet
    2. Bakholdin I.B., “Theory and Classification of the Reversible Structures of Discontinuities in Hydrodynamic-Type Models”, Pmm-J. Appl. Math. Mech., 78:6 (2014), 599–612  crossref  mathscinet  isi  scopus
    3. I. B. Bakholdin, “Issledovanie rasprostraneniya voln v trubakh s uprugimi stenkami i analiz chislennykh metodov”, Preprinty IPM im. M. V. Keldysha, 2016, 030, 32 pp.  mathnet
    4. I. B. Bakholdin, “Issledovanie modelei, opisyvayuschikh rasprostranenie voln v trube s uprugimi stenkami pri nalichii zapolneniya ee zhidkostyu i gazom”, Preprinty IPM im. M. V. Keldysha, 2017, 051, 32 pp.  mathnet  crossref
    5. Bakholdin I.B., “Application of the Theory of Reversible Discontinuities to the Investigation of Equations Describing Waves in Tubes With Elastic Walls”, Pmm-J. Appl. Math. Mech., 81:5 (2017), 409–419  crossref  mathscinet  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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