Stationary solutions to a nonlinear Schrödinger equation with potential in one dimension

2003 ◽  
Vol 133 (2) ◽  
pp. 409-437 ◽  
Author(s):  
Mihai Mariş
Keyword(s):  
Schrödinger Equation ◽  
Sound Velocity ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Nonlinear Schrodinger Equation ◽  
One Dimension ◽  
One Dimensional ◽  
Nonlinear Schrödinger ◽  
The One

We study the one-dimensional Gross-Pitaevskii-Schrödinger equation with a potential U moving at velocity v. For a fixed v less than the sound velocity, it is proved that there exist two time-independent solutions if the potential is not too big.

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