论文标题
周期性流动波的大振幅调制
Large-amplitude modulation of periodic traveling waves
论文作者
论文摘要
我们介绍了一种基于假数分析，多尺度扩展和Kreiss对称性估计值的新方法，以研究高频周期性波模式的调制方法，例如在双曲和双曲线和双曲线 - 寄生虫边界值理论中。关键成分是局部浮点变换，作为预先调节器，在背景的正常方向上删除了较大的衍生物，并使用Gardner的周期性Evans功能连接有关组件周期性波的光谱信息的使用，以阻止产生的近似恒定恒定的分辨率。我们的主要结果是在高频/小波长限制中，多振幅平面周期溶液的所有大振幅平滑调制溶液的所有阶平滑调制溶液的所有顺序调制。
We introduce a new approach to the study of modulation of high-frequency periodic wave patterns, based on pseudodifferential analysis, multi-scale expansion, and Kreiss symmetrizer estimates like those in hyperbolic and hyperbolic-parabolic boundary-value theory. Key ingredients are local Floquet transformation as a preconditioner removing large derivatives in the normal direction of background rapidly oscillating fronts and the use of the periodic Evans function of Gardner to connect spectral information on component periodic waves to block structure of the resulting approximately constant-coefficient resolvent ODEs. Our main result is bounded-time existence and valitidy to all orders of large-amplitude smooth modulations of planar periodic solutions of multi-D reaction diffusion systems in the high-frequency/small wavelength limit.
