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Semiclassical limit of the nonlinear Schrödinger equation in small time. (English) Zbl 0910.35115
Summary: We study the semi-classical limit of the nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system, and in particular the validity of the WKB method.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35C20 Asymptotic expansions of solutions to PDEs
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