We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of non-degenerate wells. These follow WKB ansatz; error is O(exp(--cN)), where c > 0 and N $\rightarrow$ +$\infty$ inverse semiclassical parameter.
We survey some recent results related to three long wave asymptotic regimes for the Nonlinear-Schrödinger Equation: the Euler regime corresponding to the WKB method, the linear wave regime and finally the KdV/KP-I asymptotic dynamics.
