Geodesic
On the exact solution of the evolution equations for two interacting narrow wave packets propagating in a non-Abelian plasma
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 159-169.

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In this paper, we present and discuss a self-consistent system of kinetic equations of the Boltzmann type, which takes into account the time evolution of soft non-Abelian plasma excitations and the mean value of the color charge in the interaction of a high-energy color-charged particle with a plasma. Based on these equations, we examine a model problem of interaction of two infinitely narrow wave packets and obtain a system of first-order nonlinear ordinary differential equations, which governs the dynamics of interacting the colorless $N^{l}_{\mathbf \kappa}$ and color $W^{l}_{\mathbf \kappa}$ components of the density of the number collective bosonic excitations. Due to the autonomy of the right-hand sides, we reduce this system to a single nonlinear Abel differential equation of the second kind. Finally, we show that at a certain ratio between the constants involved in this nonlinear equation, one can obtain an exact solution in the parametric form.
Keywords: kinetic equation, non-Abelian plasma, wave packet, Abel equation of the second kind, Lambert function 
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     title = {On the exact solution of the evolution equations for two interacting narrow wave packets propagating in a {non-Abelian} plasma},
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Yu. A. Markov; M. A. Markova; N. Yu. Markov. On the exact solution of the evolution equations for two interacting narrow wave packets propagating in a non-Abelian plasma. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 159-169. http://geodesic.mathdoc.fr/item/INTO_2024_234_a17/

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