论文标题
具有非局部立方非线性的二维动力学方程的渐近解决方案家族
Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity
论文作者
论文摘要
我们将原始的半经典方法应用于非本地立方非线性的动力电离方程，以构建其渐近溶液的家族。提出的方法依赖于所需溶液矩的辅助动力学系统，用于动力学方程和相关的线性偏微分方程。动力学方程式的渐近溶液家族是使用作用于动力学系统确定点的邻域的功能的对称算子来构建的。基于这些解决方案，我们引入了非线性动力学方程的非线性叠加原理。我们基于Maslov胚芽方法的形式主义应用于特定二维动力学方程的库奇问题。使用数值分析计算，可以作为非线性叠加获得动力学增强金属蒸气活性培养基中离子分布的演变。
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.
