Theoretical and Mathematical Physics

, Volume 91, Issue 1, pp 418–427 | Cite as

A class of exact solutions for a kinetic model of an equilibrium plasma

  • Yu. A. Markov


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.


Hydrogen Distribution Function Helium Exact Solution Kinetic Model 
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© Plenum Publishing Corporation 1992

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  • Yu. A. Markov

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