Validity of Whitham’s Equations for the Modulation of Periodic Traveling Waves in the NLS Equation
Validity of Whitham’s Equations for the Modulation of Periodic Traveling Waves in the NLS Equation
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NLS 方程中周期行波调制 Whitham 方程的有效性
DOI：
10.1007/s00332-009-9043-4
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发表时间：
2009
影响因子：
3
通讯作者：
G. Schneider
中科院分区：
文献类型：
--
作者：
Wolf‐Patrick Düll;G. Schneider
我们证明了慢调制的时间和空间的周期波列的NLS方程可以近似通过解决方案的Whitham方程与波列。误差估计是基于一个适当的选择极坐标，柯西-Kowalevskaya的存在性和唯一性定理，和能量估计。
We prove that slow modulations in time and space of periodic wave trains of the NLS equation can be approximated via solutions of Whitham’s equations associated with the wave train. The error estimates are based on a suitable choice of polar coordinates, a Cauchy–Kowalevskaya-like existence and uniqueness theorem, and energy estimates.