Semiclassical limit of the nonlinear Schrodinger equation in small time

被引：97

作者：

Grenier, E ^{[1
]}

机构：

[1] Univ Paris 06, Anal Numer Lab, CNRS, URA 189, F-75252 Paris 05, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 126卷 / 02期

关键词：

nonlinear Schrodinger equations; semiclassical limit;

D O I：

10.1090/S0002-9939-98-04164-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the semi-classical limit of the nonlinear Schrodinger equation for initial data with Sobolev regularity, before shocks appear in the limit system, and in particular the validity of the WKB method.

引用

页码：523 / 530

页数：8

共 50 条

[31] On the semiclassical limit of the focusing nonlinear Schrödinger equation
School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
不详
Phys Lett Sect A Gen At Solid State Phys, 1-2 (75-86):
[32] SEMICLASSICAL LIMIT TO THE GENERALIZED NONLINEAR SCHR?DINGER EQUATION
Boling Guo
Guoquan Qin
Annals of Applied Mathematics, 2018, 34 (03) : 221 - 243
[33] A level set method for the semiclassical limit of the Schrodinger equation with discontinuous potentials
Wei, Dongming
Jin, Shi
Tsai, Richard
Yang, Xu
JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 229 (19) : 7440 - 7455
[34] Uniform semiclassical approximations of the nonlinear Schrodinger equation by a Painleve mapping
Witthaut, D.
Korsch, H. J.
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (47): : 14687 - 14697
[35] A numerical study of the perturbed semiclassical focusing nonlinear Schrodinger equation
Bergamin, JM
Kamvissis, S
Bountis, T
PHYSICS LETTERS A, 2002, 304 (3-4) : 85 - 94
[36] Intertwining semiclassical bound states to a nonlinear magnetic Schrodinger equation
Cingolani, Silvia
Clapp, Monica
NONLINEARITY, 2009, 22 (09) : 2309 - 2331
[37] LIMIT OF THE SOLUTION OF THE NONLINEAR SCHRODINGER-EQUATION AT BLOWING-UP TIME
MERLE, F
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1987, 304 (17): : 539 - 542
[38] LIMIT OF THE SOLUTION OF A NONLINEAR SCHRODINGER-EQUATION AT BLOW-UP TIME
MERLE, F
JOURNAL OF FUNCTIONAL ANALYSIS, 1989, 84 (01) : 201 - 214
[39] Compressible limit of the nonlinear Schrodinger equation with different-degree small parameter nonlinearities
Gan, Zaihui
Guo, Boling
CHINESE ANNALS OF MATHEMATICS SERIES B, 2011, 32 (01) : 105 - 122
[40] A PARTICLE METHOD FOR THE SEMICLASSICAL LIMIT OF THE SCHRODINGER EQUATION AND THE VLASOV-POISSON EQUATIONS
Jin, Shi
Wei, Dongming
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (06) : 3259 - 3279

← 1 2 3 4 5 →