Global existence for a system of weakly coupled nonlinear Schrödinger equations

被引:0
|
作者
J. Shu
J. Zhang
机构
[1] Sichuan Normal University,Visual Computing and Virtual Reality Key Laboratory of Sichuan Province
[2] Sichuan Normal University,College of Mathematics and Software Science
来源
Mathematical Notes | 2009年 / 86卷
关键词
weakly coupled nonlinear Schrödinger equations; global existence; Gagliardo-Nirenberg inequality; Cauchy problem; Laplace operator; nonlinear optics;
D O I
暂无
中图分类号
学科分类号
摘要
This paper discusses the weakly coupled nonlinear Schrödinger equations in the supercritical case. With the best constant of the Gagliardo-Nirenberg inequality, we derive a sufficient condition for the global existence of solutions; this condition is expressed in terms of stationary solutions (nonlinear ground state).
引用
收藏
页码:650 / 654
页数:4
相关论文
共 50 条
  • [1] Energy criteria of global existence for the coupled nonlinear Schrödinger equations with harmonic potentials
    Guanggan Chen
    Yunyun Wei
    [J]. Nonlinear Differential Equations and Applications NoDEA, 2008, 15 : 195 - 208
  • [2] Global existence for a system of weakly coupled nonlinear Schrodinger equations
    Shu, J.
    Zhang, J.
    [J]. MATHEMATICAL NOTES, 2009, 86 (5-6) : 650 - 654
  • [3] Existence of the global attractor to fractional order generalized coupled nonlinear Schrödinger equations with derivative
    Wenjing Song
    Ganshan Yang
    [J]. Boundary Value Problems, 2018
  • [4] Global Attractor for a Class of Coupled Nonlinear Schrödinger Equations
    Li G.
    Zhu C.
    [J]. SeMA Journal, 2012, 60 (1) : 5 - 25
  • [5] GLOBAL EXISTENCE OF THE SOLUTION OF NONLINEAR SCHRDINGER EQUATIONS IN EXTERIOR DOMAINS
    陈韵梅
    [J]. Acta Mathematicae Applicatae Sinica, 1985, (03) : 191 - 212
  • [6] Solitons in a coupled system of fractional nonlinear Schrödinger equations
    Zeng, Liangwei
    Belic, Milivoj R.
    Mihalache, Dumitru
    Li, Jiawei
    Xiang, Dan
    Zeng, Xuanke
    Zhu, Xing
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2023, 456
  • [7] Standing waves for a coupled system of nonlinear Schrödinger equations
    Zhijie Chen
    Wenming Zou
    [J]. Annali di Matematica Pura ed Applicata (1923 -), 2015, 194 : 183 - 220
  • [8] Existence and bifurcation of solutions for a double coupled system of Schrdinger equations
    TIAN RuShun
    ZHANG ZhiTao
    [J]. Science China Mathematics, 2015, 58 (08) : 1607 - 1620
  • [9] Existence and bifurcation of solutions for a double coupled system of Schrödinger equations
    RuShun Tian
    ZhiTao Zhang
    [J]. Science China Mathematics, 2015, 58 : 1607 - 1620
  • [10] Existence and Uniqueness of Positive Solutions to Three Coupled Nonlinear Schrdinger Equations
    Guo-bei FANG
    Zhong-xue L
    [J]. Acta Mathematicae Applicatae Sinica, 2015, 31 (04) : 1021 - 1032