Geodesic
A~class of exact solutions for a~kinetic model of an equilibrium plasma
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 1, pp. 129-141

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The stationary Vlasov–Maxwell system is reduced to a “resolving” equation of sinh-Gordon type. It is shown that for fully ionized hydrogen and helium plasmas the resolving equation will have the form of the sinh-Gordon equation and Bullough–Dodd–Zhiber–Shabat equation (with elliptic operator), respectively. Hirota's method is used to obtain exact solutions for these equations. From these solutions, the characteristics of the system are recovered: the distribution functions and the self-consistent electromagnetic field. 
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     author = {Yu. A. Markov},
     title = {A~class of exact solutions for a~kinetic model of an equilibrium plasma},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {129--141},
     publisher = {mathdoc},
     volume = {91},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_1_a9/}
}
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Yu. A. Markov. A~class of exact solutions for a~kinetic model of an equilibrium plasma. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 1, pp. 129-141. http://geodesic.mathdoc.fr/item/TMF_1992_91_1_a9/