Geodesic
Magnetohydrodynamics with regard to electron inertia: Some exact solutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 3, pp. 349-361

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Magnetohydrodynamic (MHD) equations are derived with the finite electron mass taken into account. The low-frequency spectrum of a cold two-component plasma can be described using these equations. In the linear approximation, the MHD equations lead to results coinciding with those of multifluid hydrodynamics. An exact solution to the generalized MHD equations is obtained as a stationary nonlinear wave. A soliton-like solution is found for a wide range of Mach numbers and external magnetic field intensities. 
@article{TMF_1998_116_3_a2,
     author = {I. M. Aleshin},
     title = {Magnetohydrodynamics with regard to electron inertia: {Some} exact solutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {349--361},
     publisher = {mathdoc},
     volume = {116},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_116_3_a2/}
}
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I. M. Aleshin. Magnetohydrodynamics with regard to electron inertia: Some exact solutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 3, pp. 349-361. http://geodesic.mathdoc.fr/item/TMF_1998_116_3_a2/