Geometric optics with caustic crossing for some nonlinear Schrodinger equations

We underscore nonlinear phenomena when oscillations give rise to a caustic. We consider a. family of nonlinear Schrodinger equations, for which several notions of critical index appear, as for the description of the propagation outside the caustic on the one hand, and the caustic crossing on the other hand. The propagation is similar to that known by WKB method, and the caustic crossing is either the same as in the linear case, or described in terms of scattering operators. A uniform description is obtained by a generalization of the use of Lagrangian integrals.