A coupled Schrödinger system with critical exponent

2020 ◽  
Vol 59 (5) ◽  
Author(s):  
Haidong Liu ◽  
Zhaoli Liu
Keyword(s):  
Critical Exponent ◽  
Coupled Schrödinger System ◽  
Schrödinger System

Existence of positive solutions to a linearly coupled Schrödinger system with critical exponent

2018 ◽  
Vol 20 (07) ◽  
pp. 1750082 ◽  
Author(s):  
Huiling Wu ◽  
Jianqing Chen ◽  
Yongqing Li
Keyword(s):  
Critical Exponent ◽  
Positive Solution ◽  
Positive Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Coupled Schrödinger System ◽  
Nonlinear Schrodinger Equations ◽  
Existence Of Positive Solutions ◽  
Schrödinger System

We are concerned with the system of nonlinear Schrödinger equations [Formula: see text] The existence of a positive solution to the system is proved.

scholarly journals Bifurcations for a coupled Schrödinger system with multiple components

2015 ◽  
Vol 66 (5) ◽  
pp. 2109-2123 ◽  
Author(s):  
Thomas Bartsch ◽  
Rushun Tian ◽  
Zhi-Qiang Wang
Keyword(s):  
Coupled Schrödinger System ◽  
Multiple Components ◽  
Schrödinger System

Schrödinger systems with quadratic interactions

2019 ◽  
Vol 21 (08) ◽  
pp. 1850077
Author(s):  
Rushun Tian ◽  
Zhi-Qiang Wang ◽  
Leiga Zhao
Keyword(s):  
Variational Formulation ◽  
Variational Problems ◽  
Nontrivial Solutions ◽  
New Techniques ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Coupled Schrödinger System ◽  
Schrödinger Systems ◽  
Bose Einstein ◽  
Schrödinger System

In this paper, we consider the existence and multiplicity of nontrivial solutions to a quadratically coupled Schrödinger system [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants and [Formula: see text], [Formula: see text]. Such type of systems stem from applications in nonlinear optics, Bose–Einstein condensates and plasma physics. The existence (and nonexistence), multiplicity and asymptotic behavior of vector solutions of the system are established via variational methods. In particular, for multiplicity results we develop new techniques for treating variational problems with only partial symmetry for which the classical minimax machinery does not apply directly. For the above system, the variational formulation is only of even symmetry with respect to the first component [Formula: see text] but not with respect to [Formula: see text], and we prove that the number of vector solutions tends to infinity as [Formula: see text] tends to infinity.

scholarly journals Vector Solitons of a Coupled Schrödinger System with Variable Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Juan Carlos Muñoz Grajales
Keyword(s):  
Numerical Simulations ◽  
Finite Energy ◽  
Variable Coefficients ◽  
Soliton Equations ◽  
Nonlinear Schrödinger ◽  
Coupled Schrödinger System ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

We show the existence of waveforms of finite-energy (vector solitons) for a coupled nonlinear Schrödinger system with inhomogeneous coefficients. Furthermore, some of these solutions are approximated using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the corresponding soliton equations. Some numerical simulations concerned with analysis of a collision of two oncoming vector solitons of the system are also performed.

Stabilization of the weakly coupled Schrödinger system

2020 ◽  
pp. 1-14
Author(s):  
Xiaoyu Fu ◽  
Hualei Zhang ◽  
Xianzheng Zhu
Keyword(s):  
Coupled Schrödinger System ◽  
Weakly Coupled ◽  
Schrödinger System
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