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Certain exact solutions of the kinetic model of quark-plasma equilibrium in the Abelian-dominance approximation. (English. Russian original) Zbl 0890.35119
Phys.-Dokl. 40, No. 12, 609-612 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 5, 601-604 (1994).
We reduce the time-depenent kinetic equations for a two-flux quark plasma (QP) in the Abelian-dominance approximation with respect to nonlinear equations of three types: the Toda $$A_2$$-periodic chain, Bullough-Dodda-Zhiber-Shabat, and double sinh-Gordon (with an elliptic operator). Using the solutions of these equations obtained on the basis of the Hirota method and substitutions, we reconstruct the QP input characteristics: the distribution functions and the potential of the self-consistent field.
##### MSC:
 35Q40 PDEs in connection with quantum mechanics 82B10 Quantum equilibrium statistical mechanics (general) 81V25 Other elementary particle theory in quantum theory