Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Semiclassical limit of the nonlinear Schrödinger equation in small time

Author(s): E. Grenier
Journal: Proc. Amer. Math. Soc. 126 (1998), 523-530.
MSC (1991): Primary 35Q55, 35C20
MathSciNet review: 1425123
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Abstract: 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.

References:

1.: P. Gérard, Remarques sur l'analyse semi-classique de l'équation de Schrödinger non linéaire, Séminaire EDP de l'École Polytechnique, Palaiseau, France (1992-93), lecture $n^{o}$ XIII. MR 94i:35157
2.: J. Ginibre, G. Velo, On the global Cauchy problem for some nonlinear Schrödinger equation, Ann. Inst. H. Poincaré, Anal. non linéaire 1 (1984), 309-323. MR 87a:35164
3.: E. Grenier, Limite semiclassique de l'équation de Schrödinger non linéaire en temps petit, C.R. Acad. Sci. Paris, Série I 320 (1995), 691-694. MR 96a:35191
4.: S. Jin, C. D. Levermore, D.W. Mc Laughlin, The behaviour of solutions of the NLS equation in the semiclassical limit, Singular limits of dispersive waves, NATO ASI, Series B : Physics, vol. 320, 1994, pp. 235-256. MR 95k:35191
5.: A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Appl. Math. Sci 53, Springer, 1984. MR 85e:35077

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