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This project is articulated around to directions: semi-classical limit, and long time behavior, for nonlinear Schrödinfer equations. The first direction is subdivided into supercritical WKB regime (need of a new model beyond singularities for the Euler equation), critical WKB regime (and link with the Cauchy problem on the one hand, and Physics on the other hand), the propagation of wave packets, and instabilities. The second direction is concerned with dynamical properties of the nonlinear scattering operator, the role of geometry, vortex filaments, and solitons for the Gross-Pitaevskii equation.
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