Testing by wave packets and modified scattering in nonlinear dispersive pde’s
Testing by wave packets and modified scattering in nonlinear dispersive pde’s
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DOI：
10.1090/btran/148
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
M. Ifrim;D. Tataru
中科院分区：
文献类型：
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作者：
M. Ifrim;D. Tataru
在研究非线性色散偏微分方程的全局性质时，当解在无穷远处衰减到临界值时，会遇到修正的散射现象，而散射现象几乎不存在。一个有趣的例子是，在一个空间维度的立方非线性问题。作者引入了波包测试方法，作为有效捕获与此类流动相关的渐进方程的工具，从而以更简单、更有效的方式和较低的规则性建立修改的散射机制。在这些简要说明中，我们描述了如何将这种方法应用于一般色散关系的问题。
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.