WKB expansion for a fractional Schrödinger equation with applications to controllability

PDF version | Download Matlab Code… In [3], we develop a WKB analysis for the propagation of the solutions to the following one-dimensional nonlocal Schrödinger equation \begin{align}\label{main_eq} \mathcal{P}_s u:= \left[i\partial_t + \ffl{s}{}\right]u = 0, &\;\; (x,t)\in\RR\times(0,+\infty), \end{align} with highly oscillatory initial datum \begin{align}\label{in_dat} u(x,0) = u_{\textrm{\small in}}(x) e^{i\frac{\xi_0}{\varepsilon} x}:=u_0(x),\;\;\; \xi_0\in\RR. \end{align} In (\ref{main_eq}), $\ffl{s}{}$ is…