Geodesic
Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 515-528 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{ZVMMF_2011_51_3_a9,
     author = {I. B. Bakholdin and E. R. Egorova},
     title = {Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {515--528},
     year = {2011},
     volume = {51},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a9/}
}
TY  - JOUR
AU  - I. B. Bakholdin
AU  - E. R. Egorova
TI  - Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 515
EP  - 528
VL  - 51
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a9/
LA  - ru
ID  - ZVMMF_2011_51_3_a9
ER  - 
%0 Journal Article
%A I. B. Bakholdin
%A E. R. Egorova
%T Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 515-528
%V 51
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a9/
%G ru
%F ZVMMF_2011_51_3_a9
I. B. Bakholdin; E. R. Egorova. Study of magnetosonic solitary waves for the electron magnetohydrodynamics equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 515-528. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a9/

[1] Kakutani T., Ono H., “Weak non-linear hydromagnetic waves in a cold collision-free plasma”, J. Phys. Soc. Japan, 26 (1969), 1305–1318 | DOI

[2] Il'ichev A., “Steady waves in a cold plasma”, J. Plasma Phys., 55:2 (1996), 181–194 | DOI | MR

[3] Bakholdin I., Il'ichev A., “Solitary-wave decay in a cold plasma”, J. Plasma Phys., 60:3 (1998), 569–580 | DOI

[4] Bakholdin I., Il'ichev A., Zharkov A., “Steady magnetoacoustic waves and decay of solitonic structures in finite beta plasma”, J. Plasma Phys., 67:1 (2002), 1–26 | DOI | MR

[5] Bakholdin I. B., Zharkov A. A., Ilichev A. T., “Neustoichivost solitonov i frontov v izotropnoi besstolknovitelnoi kvazi-neitralnoi plazme s izotermicheskim davleniem”, Zh. tekhn. fiz., 118:1(7) (2000), 125–141

[6] Ilichev A. T., Uedinennye volny v modelyakh gidromekhaniki, Fizmatlit, M., 2003

[7] Bakholdin I. B., Bezdissipativnye razryvy v mekhanike sploshnoi sredy, Fizmatlit, M., 2004

[8] Kingsepp A. S., Vvedenie v nelineinuyu fiziku plazmy, Izd-vo MFTI, M., 1996

[9] Donatelli D., Marcati P., “Application of dispersive estimates to the acoustic pressure waves for incompressible fluid problems”, Proc. Symp. Appl. Math., 67:1 (2009), 279–297 | MR | Zbl

[10] Rouch P. Dzh., Vychislitelnaya gidrodinamika, Mir, M., 1980 | Zbl

[11] Kalodzhero F., Degasperis A., Spektralnye preobrazovaniya i solitony. Metody resheniya i issledovaniya nelineinykh evolyutsionnykh uravnenii, Mir, M., 1985, 472 pp. | MR

[12] Bakholdin I. B., “Zadacha o raspade uedinennykh voln i razryvy”, Izv. RAN. Mekhan. zhidkosti i gaza, 2005, no. 6, 122–139 | MR | Zbl

[13] Bakholdin I. B., “Volnovye razryvy, opisyvaemye modifitsirovannym uravneniem Shredingera”, Zh. vychisl. matem. i matem. fiz., 38:8 (1998), 1331–1350 | MR

[14] Bakholdin I. B., “Skachok s izlucheniem v modelyakh, opisyvaemykh obobschennym uravneniem Kortevega–de Vriza”, Prikl. matem. i mekhan., 65:1 (2001), 59–68 | MR | Zbl

[15] Bakholdin I. B., “Metody issledovaniya struktur dissipativnykh i bezdissipativnykh razryvov v sistemakh s dispersiei”, Zh. vychisl. matem. i matem. fiz., 45:2 (2005), 330–343 | MR | Zbl