非线性色散wave equations多尺度方法的数值精度
On the numerical accuracy of the method of multiple scales for nonlinear dispersive wave equations
摘要：
本文利用多尺度方法研究色散波动方程，并通过数值试验验证了该方法的精度。我们的MMS解决方案的主要特点是振幅方程的线性和时频的复杂性。MMS测试作为一个初值问题使用三种选择的色散模型，一个玩具和两个洛伦兹模型。根据问题的参数，振幅方程可以是适定的或不适定的。尽管不适定性，MMS解决方案仍然是一个有效的近似的解决方案，原来的非线性模型。
英文摘要：
In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and the complex nature of the time-frequency. The MMS is tested as an initial value problem using three choices of the dispersion model, one toy and two Lorentz models. Depending on the parameters of the problem, the amplitude equation can be both well- or ill-posed. Despite the ill-posedness, the MMS solution remains a valid approximation of the solution to the original nonlinear model.
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