Family of Asymptotic Solutions to the Two-Dimensional Kinetic Equation with a Nonlocal Cubic Nonlinearity / A. V. Shapovalov, A. E. Kulagin, S. A. Sinyukov
Уровень набора: SymmetryЯзык: английский.Страна: .Резюме или реферат: We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach proposed relies on an auxiliary dynamical system of moments of the desired solution to the kinetic equation and the associated linear partial differential equation. The family of asymptotic solutions to the kinetic equation is constructed using the symmetry operators acting on functions concentrated in a neighborhood of a point determined by the dynamical system. Based on these solutions, we introduce the nonlinear superposition principle for the nonlinear kinetic equation. Our formalism based on the Maslov germ method is applied to the Cauchy problem for the specific two-dimensional kinetic equation. The evolution of the ion distribution in the kinetically enhanced metal vapor active medium is obtained as the nonlinear superposition using the numerical-analytical calculations..Примечания о наличии в документе библиографии/указателя: [References: 29 tit.].Тематика: электронный ресурс | труды учёных ТПУ | kinetic model | symmetry operators | Maslov germ | nonlinear superposition principle | dense plasma | active media | semiclassical approximation | WKB–Maslov method | кинетические модели | плотная плазма | квазиклассическое приближение | ионизация | кинетические уравнения | метод Маслова Ресурсы он-лайн:Щелкните здесь для доступа в онлайн | Щелкните здесь для доступа в онлайнTitle screen
[References: 29 tit.]
We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach proposed relies on an auxiliary dynamical system of moments of the desired solution to the kinetic equation and the associated linear partial differential equation. The family of asymptotic solutions to the kinetic equation is constructed using the symmetry operators acting on functions concentrated in a neighborhood of a point determined by the dynamical system. Based on these solutions, we introduce the nonlinear superposition principle for the nonlinear kinetic equation. Our formalism based on the Maslov germ method is applied to the Cauchy problem for the specific two-dimensional kinetic equation. The evolution of the ion distribution in the kinetically enhanced metal vapor active medium is obtained as the nonlinear superposition using the numerical-analytical calculations.
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