Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Semiclassical limit of the nonlinear
Schrödinger equation in small time


Author: E. Grenier
Journal: Proc. Amer. Math. Soc. 126 (1998), 523-530
MSC (1991): Primary 35Q55, 35C20
MathSciNet review: 1425123
Full-text PDF Free Access

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 [Enhancements On Off] (What's this?)

  • 1. P. Gérard, Remarques sur l’analyse semi-classique de l’équation de Schrödinger non linéaire, Séminaire sur les Équations aux Dérivées Partielles, 1992–1993, École Polytech., Palaiseau, 1993, pp. Exp.\ No.\ XIII, 13 (French). MR 1240554 (94i:35157)
  • 2. J. Ginibre and G. Velo, On the global Cauchy problem for some nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 4, 309–323 (English, with French summary). MR 778977 (87a:35164)
  • 3. Emmanuel Grenier, Limite semi-classique de l’équation de Schrödinger non linéaire en temps petit, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 6, 691–694 (French, with English and French summaries). MR 1323939 (96a:35191)
  • 4. Shan Jin, C. David Levermore, and David W. McLaughlin, The behavior of solutions of the NLS equation in the semiclassical limit, Singular limits of dispersive waves (Lyon, 1991) NATO Adv. Sci. Inst. Ser. B Phys., vol. 320, Plenum, New York, 1994, pp. 235–255. MR 1321208 (95k:35191)
  • 5. A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol. 53, Springer-Verlag, New York, 1984. MR 748308 (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: http://dx.doi.org/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
Article copyright: © Copyright 1998 American Mathematical Society