标题： 非线性薛定谔方程的超临界几何光学 显示英文标题

标题： Supercritical geometric optics for nonlinear Schrodinger equations

摘要： 我们考虑带有非聚焦、光滑非线性的非线性薛定谔方程的小时间半经典极限。 对于超三次非线性，由于真空的存在，极限系统并非直接双曲。 为解决此问题，我们引入了新的未知函数，这些函数以波函数本身为基准进行非线性定义。 这种方法提供了Y.Brenier提出的调制能量泛函的一个局部版本。 我们得到的系统是双曲对称的，WKB分析的合理性随之得到验证。 显示英文摘要

摘要： We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local version of the modulated energy functional introduced by Y.Brenier. The system we obtain is hyperbolic symmetric, and the justification of WKB analysis follows.