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 
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/
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     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/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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