Markov, Yu. A.; Markova, M. A. 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 Keywords:kinetic equations for a two-flux quark plasma; Hirota method; input characteristics PDF BibTeX XML Cite \textit{Yu. A. Markov} and \textit{M. A. Markova}, Phys.-Dokl. 40, No. 12, 1 (1994; Zbl 0890.35119); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 5, 601--604 (1994)