Coupled nonlinear Schrödinger equations with harmonic potential

The initial value problem for a coupled nonlinear Schrödinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. In the focusing case, the existence and stability/instability of standing waves are established. Moreover, global well-posedness i...

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 7; no. 3; pp. 195 - 218
Main Authors Hezzi, H., Nour, M. M., Saanouni, T.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2018
Springer
Springer Nature B.V
Subjects
Boundary value problems
Defocusing
Energy
Mathematical research
Mathematics
Mathematics and Statistics
Nonlinear equations
Schrodinger equation
Schrödinger equation
Stability
Standing waves
Well posed problems
35Q55
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Summary:The initial value problem for a coupled nonlinear Schrödinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. In the focusing case, the existence and stability/instability of standing waves are established. Moreover, global well-posedness is discussed via the potential well method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-017-0192-2