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

doi:10.1016/S0252-9602(15)30047-3

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1163-1188.doi: 10.1016/S0252-9602(15)30047-3

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

甘在会^1,2, 郭柏灵³, 蒋芯⁴

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;
4. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China

收稿日期:2013-09-29 修回日期:2014-12-26 出版日期:2015-09-01 发布日期:2015-09-01
作者简介:Zaihui GAN, E-mail: ganzaihui2008cn@tju.edu.cn, ganzaihui2008cn@hotmail.com Boling GUO, E-mail: gbl@iapcm.ac.cn; Xin JIANG, E-mail: jiangxin9099@sina.cn
基金资助:
This paper is supported by National Natural Science Foundation of China (11171241), Program for New Century Excellent Talents in University (NCET-12-1058).

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

Zaihui GAN^1,2, Boling GUO³, Xin JIANG⁴

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;
4. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China

Received:2013-09-29 Revised:2014-12-26 Online:2015-09-01 Published:2015-09-01
Supported by:
This paper is supported by National Natural Science Foundation of China (11171241), Program for New Century Excellent Talents in University (NCET-12-1058).

摘要/Abstract

摘要：

The existence and orbital instability of standing waves for the generalized threedimensional nonlocal nonlinear Schrödinger 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.

关键词: nonlocal nonlinear Schrö, dinger equations, standing waves, orbital instability

Abstract:

Key words: nonlocal nonlinear Schrö, dinger equations, standing waves, orbital instability

中图分类号:

35B35

甘在会, 郭柏灵, 蒋芯. ORBITAL INSTABILITY OF STANDING WAVES FOR THE GENERALIZED 3D NONLOCAL NONLINEAR SCHRÖDINGER EQUATIONS[J]. 数学物理学报(英文版), 2015, 35(5): 1163-1188.

Zaihui GAN, Boling GUO, Xin JIANG. ORBITAL INSTABILITY OF STANDING WAVES FOR THE GENERALIZED 3D NONLOCAL NONLINEAR SCHRÖDINGER EQUATIONS[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1163-1188.

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

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

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