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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.

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