论文标题
Sobolev空间中双曲线Whitham调制方程的有效性
Validity of the hyperbolic Whitham modulation equations in Sobolev spaces
论文作者
论文摘要
事实证明，在自然时间尺度上，在双曲线情况下，Whitham调制方程的解决方案（在双曲线情况下，在deocuss docuss docuss trabs的时间和空间）可以通过溶液调制方程的溶液来近似。错误估计基于实际线上的Sobolev空间中的存在，唯一性和能量参数。证据的重要组成部分是将高阶校正包括在WHITHAM理论中，以及伴随的高阶能量估计。
It is proved that modulation in time and space of periodic wave trains, of the defocussing nonlinear Schrödinger equation, can be approximated by solutions of the Whitham modulation equations, in the hyperbolic case, on a natural time scale. The error estimates are based on existence, uniqueness, and energy arguments, in Sobolev spaces on the real line. An essential part of the proof is the inclusion of higher-order corrections to Whitham theory, and concomitant higher-order energy estimates.
