Schrödinger Systems

1996 ◽  
pp. 151-173
Author(s):  
Robert Aebi
Keyword(s):  
Schrödinger Systems

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 Nonlinear Schrodinger systems: continuous and discrete

Scholarpedia ◽  
2008 ◽  
Vol 3 (8) ◽  
pp. 5561 ◽  
Author(s):  
Mark Ablowitz ◽  
Barbara Prinari
Keyword(s):  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems ◽  
Schrödinger Systems

scholarly journals Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d≥ 3 equations

2016 ◽  
Vol 271 (8) ◽  
pp. 2247-2273 ◽  
Author(s):  
Simão Correia ◽  
Filipe Oliveira ◽  
Hugo Tavares
Keyword(s):  
Ground States ◽  
Schrödinger Systems

Existence of constrained minimizer for a quadratically coupled Schrödinger systems

2018 ◽  
Vol 99 (1) ◽  
pp. 29-39
Author(s):  
Zhanping Liang ◽  
Jintao Liu
Keyword(s):  
Schrödinger Systems
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