论文标题
通过波数据包进行测试和非线性色散PDE的修饰散射
Testing by wave packets and modified scattering in nonlinear dispersive pde's
论文作者
论文摘要
在非线性分散偏微分方程的全球性能研究中，在无穷大的衰减是边界和散射几乎没有失败的情况下，遇到了修改的散射现象。一个有趣的例子是一个空间维度中立方非线性的问题。 作者引入了通过波数据包进行测试的方法，作为有效捕获与此类流相关的渐近方程的工具，从而以更简单，更有效的方式和较低的规律性建立了修改的散射机制。在这些说明性注释中，我们描述了如何将此方法应用于一般分散关系的问题。
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely. An interesting example is that of problems with cubic nonlinearities in one space dimension. The method of testing by wave packets was introduced by the authors as a tool to efficiently capture the asymptotic equations associated to such flows, and thus establish the modified scattering mechanism in a simpler, more efficient fashion, and at lower regularity. In these expository notes we describe how this method can be applied to problems with general dispersion relations.
