论文标题
分析框架中对数非线性Schrodinger方程的WKB分析
WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework
论文作者
论文摘要
我们对对数的非线性schrödinger方程的WKB分析感兴趣，该方程在半经典制度的分析框架中具有“ Riemann类样”变量。我们表明，库奇的问题在半经典常数中均匀地构成，并且可以执行半经典极限。特别是，我们的框架不仅与对数非线性的Gross-pitaevskii方程兼容，而且还允许在Infinity时允许收敛到$ 0 $的初始数据（和解决方案）。
We are interested in a WKB analysis of the Logarithmic Non-Linear Schrödinger Equation with "Riemann-like" variables in an analytic framework in semiclassical regime. We show that the Cauchy problem is locally well posed uniformly in the semiclassical constant and that the semiclassical limit can be performed. In particular, our framework is not only compatible with the Gross-Pitaevskii equation with logarithmic nonlinearity, but also allows initial data (and solutions) which can converge to $0$ at infinity.
