ORBITAL INSTABILITY OF STANDING WAVES FOR THE GENERALIZED 3D NONLOCAL NONLINEAR SCHRODINGER EQUATIONS

The existence and orbital instability of standing waves for the generalized three- dimensional nonlocal nonlinear SchrSdinger equations is studied. By defining some suitable functionals and a constrained variational problem, we first establish the existence of standing waves, which relys on the inne...

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Bibliographic Details
Published inActa mathematica scientia Vol. 35; no. 5; pp. 1163 - 1188
Main Author 甘在会 郭柏灵 蒋芯
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2015
Subjects
35B35
35J50
35Q55
nonlocal nonlinear Schrödinger equations
orbital instability
standing waves
三维
不稳定性
局部非线性
广义
能量守恒定律
薛定谔方程组
轨道
非线性Schrodinger方程
35Q55
standing waves
nonlocal nonlinear Schrödinger equations
35J50
35B35
orbital instability
Online AccessGet full text
ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(15)30047-3

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Summary:The existence and orbital instability of standing waves for the generalized three- dimensional nonlocal nonlinear SchrSdinger equations is studied. By defining some suitable functionals and a constrained variational problem, we first establish the existence of standing waves, which relys on the inner structure of the equations under consideration to overcome the drawback that nonlocal terms violate the space-scale invariance. We then show the orbital instability of standing waves. The arguments depend upon the conservation laws of the mass and of the energy.
Bibliography:42-1227/O
nonlocal nonlinear SchrSdinger equations; standing waves; orbital instability
Zaihui GAN, Boling GUO, Xin JIANG（1.Center for Applied Mathematics, Tianjin University, Tianjin 300072, China; 2.College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China;3 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China）
The existence and orbital instability of standing waves for the generalized three- dimensional nonlocal nonlinear SchrSdinger equations is studied. By defining some suitable functionals and a constrained variational problem, we first establish the existence of standing waves, which relys on the inner structure of the equations under consideration to overcome the drawback that nonlocal terms violate the space-scale invariance. We then show the orbital instability of standing waves. The arguments depend upon the conservation laws of the mass and of the energy.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(15)30047-3