|
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
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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
 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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
35Q55, 35C20
Retrieve articles in all Journals with MSC
(1991):
35Q55, 35C20
Additional Information:
E.
Grenier
Affiliation:
Laboratoire d'Analyse Numérique, CNRS - URA 189, Université Paris 6, 4 place Jussieu, 75252 Paris Cedex 05, France
Email:
grenier@ann.jussieu.fr
DOI:
10.1090/S0002-9939-98-04164-1
PII:
S 0002-9939(98)04164-1
Keywords:
Nonlinear Schr\"{o}dinger equations,
semiclassical limit
Received by editor(s):
August 13, 1996
Communicated by:
Jeffrey B. Rauch
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org