Global smooth solution to a coupled Schrödinger system in atomic Bose-Einstein condensates with two-dimensional spaces

2016 ◽  
Vol 11 (6) ◽  
pp. 1515-1532 ◽  
Author(s):  
Boling Guo ◽  
Qiaoxin Li
Keyword(s):  
Smooth Solution ◽  
Two Dimensional ◽  
Global Smooth Solution ◽  
Coupled Schrödinger System ◽  
Bose Einstein ◽  
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.

Bose-Einstein coherence in two-dimensional superfluidH4e

2008 ◽  
Vol 78 (2) ◽  
Author(s):  
S. O. Diallo ◽  
J. V. Pearce ◽  
R. T. Azuah ◽  
J. W. Taylor ◽  
H. R. Glyde
Keyword(s):  
Two Dimensional ◽  
Bose Einstein
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