论文标题
在带有$χ^3 $非线性响应的光学材料中出现的NLS系统散射和爆炸的鲜明条件
Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with $χ^3$ nonlinear response
论文作者
论文摘要
我们研究了具有立方相互作用的非线性Schrödinger方程系统的渐近动力学，在非线性光学元件中产生。我们提供尖锐的阈值标准，导致全局良好的解决方案和散射，以及在（各向异性）对称初始数据的有限时间内形成奇异性。游离渐近结果通过摩拉维兹和摩拉维兹估计值证明。通过组合变分分析和一个ODE参数来显示爆炸结果，从而克服了基于病毒型身份的凸参数的不可用。
We study the asymptotic dynamics for solutions to a system of nonlinear Schrödinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold criteria leading to global well-posedness and scattering of solutions, as well as formation of singularities in finite time for (anisotropic) symmetric initial data. The free asymptotic results are proved by means of Morawetz and interaction Morawetz estimates. The blow-up results are shown by combining variational analysis and an ODE argument, which overcomes the unavailability of the convexity argument based on virial-type identities.
