Searchlight asymptotics for high-frequency scattering by boundary inflection
Searchlight asymptotics for high-frequency scattering by boundary inflection
复制标题
通过边界拐点实现高频散射的探照灯渐近
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
I. Kamotski
中科院分区：
文献类型：
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作者：
V. Smyshlyaev;I. Kamotski
研究了边界拐点对回音壁高频渐近模式散射的内问题。薛定谔方程在半直线上的相关边值问题在空间和时间上都是线性的，这是描述从模态到散射渐近模式转变的基础，尽管已经深入研究了几十年，但在很大程度上仍然没有解决。的解决方案过去的拐点被证明有一个“探照灯”的渐近对应的光束集中在极限光线附近。建立了相关探照灯振幅的某些衰减和平滑特性。上述结果的进一步解释也进行了讨论：相关的广义波算子的存在，和一个版本的一元散射算子连接的模式和分散的渐近制度。
The paper is devoted to an inner problem for a whispering gallery high-frequency asymptotic mode’s scattering by a boundary inflection. The related boundary-value problem for a Schrödinger equation on a half-line with a potential linear in both space and time turns out to be fundamental for describing transitions from modal to scattered asymptotic patterns, and despite having been intensively studied over several decades remains largely unsolved. The solution past the inflection point is shown to have a “searchlight” asymptotics corresponding to a beam concentrated near the limit ray. Certain decay and smoothness properties of the related searchlight amplitude are established. Further interpretations of the above result are also discussed: the existence of the associated generalized wave operator, and of a version of a unitary scattering operator connecting the modal and scattered asymptotic regimes.