  For the semi-classical limit of the cubic, defocusing nonlinear Schrodinger
equation with an external potential, we explain the notion of criticality
before a caustic is formed. In the sub-critical and critical cases, we justify
the WKB approximation. In the super-critical case, the WKB analysis provides a
new phenomenon for the (classical) cubic, defocusing nonlinear Schrodinger
equation, which can be compared to the loss of regularity established for the
nonlinear wave equation by G. Lebeau. We also show some instabilities at the
semi-classical level.
