单波模型中的非线性密度波
Nonlinear Density Waves in the Single-Wave Model
摘要：
利用与水囊模型相对应的Vlasov方程的一类解，将单波模型方程转化为精确的水动力学封闭。然后用重整化群方法对热流体动力学方程进行处理。结果，振幅方程的缓变波振幅的推导。由于波的特征方程一般有三个根，因此我们考察了两种情况。如果特征方程的所有三个根都是实数，则本征模的振幅方程表示三个耦合非线性方程的系统。当色散方程具有一个实共轭根和两个复共轭根时，振幅方程为两个复系数耦合方程。分析结果进行比较，通过数值求解流体动力学方程得到的精确的系统动力学。
英文摘要：
The single-wave model equations are transformed to an exact hydrodynamic closure by using a class of solutions to the Vlasov equation corresponding to the waterbag model. The warm fluid dynamic equations are then manipulated by means of the renormalization group method. As a result, amplitude equations for the slowly varying wave amplitudes are derived. Since the characteristic equation for waves has in general three roots, two cases are examined. If all three roots of the characteristic equation are real, the amplitude equations for the eigenmodes represent a system of three coupled nonlinear equations. In the case, where the dispersion equation possesses one real and two complex conjugate roots, the amplitude equations take the form of two coupled equations with complex coefficients. The analytical results are then compared to the exact system dynamics obtained by solving the hydrodynamic equations numerically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
