一类非线性方程焦散点聚焦问题
Focusing at a point with caustic crossing for a class of nonlinear equations
摘要：
研究了非线性偏微分方程在短波长极限下解的渐近性态。对于引起聚焦在一点的初始数据，我们突出了关键指标，就焦散线附近的非线性的影响而言。我们的结果推广了第一作者在非线性薛定谔方程情形下证明的一些结果。我们将它们应用到Hartree，Klein-Gordon和波动方程。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
