一种在同时高等离子频率和亚音速极限区域中均匀且最优准确的Klein-Gordon-Zakharov系统数值方法
A uniformly and optimally accurate method for the Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime
AI总结：
本文提出了一种均匀且最优准确的数值方法，用于求解具有两个无量纲参数的Klein-Gordon-Zakharov系统，在同时高等离子频率和亚音速极限区域中，该方法能够有效处理由参数反比于等离子频率和声速导致的波传播问题。
摘要：
我们提出了一种均匀且最优准确的数值方法，用于求解具有两个无量纲参数$0<ε\le1$和$0<γ\le 1$的Klein-Gordon-Zakharov（KGZ）系统，这两个参数分别反比于等离子频率和声速。在同时高等离子频率和亚音速极限区域（即$ε<γ\to 0^+$）中，KGZ系统退化为一个立方Schrödinger方程，解在时间中传播具有$O(ε^2)$波长的波，同时由于初始数据的不兼容性，在空间中包含快速向外传播的初始层，速度为$O(1/γ)$。通过提出KGZ系统的多尺度分解，我们提出了一种多尺度时间积分傅里叶伪谱方法，该方法是显式、高效且均匀准确的，适用于所有$0<ε<γ\leq1$的KGZ系统求解。数值结果展示了该方法的效率和精度。最后，该方法应用于研究当$ε<γ\to 0^+$时KGZ系统对其极限模型的收敛率。
英文摘要：
We present a uniformly and optimally accurate numerical method for solving the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters $0<ε\le1$ and $0<γ\le 1$, which are inversely proportional to the plasma frequency and the acoustic speed, respectively. In the simultaneous high-plasma-frequency and subsonic limit regime, i.e. $ε<γ\to 0^+$, the KGZ system collapses to a cubic Schrödinger equation, and the solution propagates waves with $O(ε^2)$-wavelength in time and meanwhile contains rapid outgoing initial layers with speed $O(1/γ)$ in space due to the incompatibility of the initial data. By presenting a multiscale decomposition of the KGZ system, we propose a multiscale time integrator Fourier pseduospectral method which is explicit, efficient and uniformly accurate for solving the KGZ system for all $0<ε<γ\leq1$. Numerical results are reported to show the efficiency and accuracy of scheme. Finally, the method is applied to investigate the convergence rates of the KGZ system to its limiting models when $ε<γ\to 0^+$.
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