scholarly journals Strang splitting for a semilinear Schrödinger equation with damping and forcing

2017 ◽  
Vol 455 (2) ◽  
pp. 1051-1071 ◽  
Author(s):  
Tobias Jahnke ◽  
Marcel Mikl ◽  
Roland Schnaubelt
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Strang Splitting ◽  
Semilinear Schrödinger Equation

On the semilinear Schrödinger equation with time dependent coefficients

2014 ◽  
Vol 287 (17-18) ◽  
pp. 1986-2001
Author(s):  
Takuya Gonda ◽  
Shuji Machihara ◽  
Tohru Ozawa
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Semilinear Schrödinger Equation

scholarly journals ON THE LOCATION OF SPIKES FOR THE SCHRÖDINGER EQUATION WITH ELECTROMAGNETIC FIELD

2005 ◽  
Vol 07 (02) ◽  
pp. 251-268 ◽  
Author(s):  
SIMONE SECCHI ◽  
MARCO SQUASSINA
Keyword(s):  
Electromagnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
External Electromagnetic Field ◽  
Power Type ◽  
Wave Solutions ◽  
Semilinear Schrödinger Equation ◽  
Ground Energy

We consider the standing wave solutions of the three dimensional semilinear Schrödinger equation with competing potential functions V and K and under the action of an external electromagnetic field B. We establish some necessary conditions for a sequence of such solutions to concentrate, in two different senses, around a given point. In the particular but important case of nonlinearities of power type, the spikes locate at the critical points of a smooth ground energy map independent of B.

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