Focusing at a point with caustic crossing for a class of nonlinear equations
Focusing at a point with caustic crossing for a class of nonlinear equations
复制标题
聚焦于一类非线性方程的焦散交叉点
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
D. Lannes
中科院分区：
文献类型：
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作者：
R. Carles;D. Lannes
研究了非线性偏微分方程在短波长的极限下解的渐近性质。对于在一点上引起聚焦的初始数据，我们突出了关键指标，因为它涉及到焦散邻近非线性的影响。我们的结果推广了第一作者在非线性薛定谔方程中所证明的一些结果。我们将它们应用于哈特里方程，克莱因-戈登方程和波动方程。
We consider the asymptotic behavior of solutions to nonlinear partial differential equations in the limit of short wavelength. For initial data which cause focusing at one point, we highlight critical indexes as far as the influence of the nonlinearity in the neighborhood of the caustic is concerned. Our results generalize some previous ones proved by the first author in the case of nonlinear Schrodinger equations. We apply them to Hartree, Klein-Gordon and wave equations.