Diffractive nonlinear geometric optics
Diffractive nonlinear geometric optics
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衍射非线性几何光学
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
J. Rauch
中科院分区：
文献类型：
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作者：
P. Donnat;J. Joly;G. Métivier;J. Rauch
这是分析双曲型偏微分方程随时间尺度的高频解的系列文章中的第一篇，超出了几何光学近似有效的范围。在这里和在[DR 2]中，我们处理可以构造具有无穷小残差的近似解的问题。关键假设是存在一个基本的线性相位，非线性是奇数，并且轮廓或包络的频谱包含在奇数中。在[JMR 6]中，讨论了不满足这些假设的问题。在这些更一般的问题中，分析了纠正的效果。
This is the first of a series of articles analysing high frequency solutions of of hyperbolic partial differential equations over time scales beyond those for which the geometric optics approximation is valid. Here and in [DR 2], we treat problems for which approximate solutions with infinitely small residual can be constructed. Key hypotheses are that there is one fundamental linear phase, the nonlinearities are odd, and the spectrum of the profiles or envelopes are contained in the odd integers. In [JMR 6] problems not satisfying these hypotheses are discussed. In those more general problems rectification effects are analysed.