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Remarks on the semiclassical analysis of the nonlinear Schrödinger equation. (Remarques sur l’analyse semi-classique de l’équation de Schrödinger non linéaire.) (French) Zbl 0874.35111
The paper discusses the semi-classical limit of the time-dependent nonlinear Schrödinger equation. Given an analytical nonlinearity, the main result is an expansion of the solution at time $$t$$ times the classical phase function in powers of $$h$$. The formula is given with an estimate on the occuring error and its validity. At the end, the author supplies a list of open questions.

##### MSC:
 35Q55 NLS equations (nonlinear Schrödinger equations) 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory