scholarly journals Justification of the nonlinear Schrödinger equation in spatially periodic media

2006 ◽  
Vol 57 (6) ◽  
pp. 905-939 ◽  
Author(s):  
Kurt Busch ◽  
Guido Schneider ◽  
Lasha Tkeshelashvili ◽  
Hannes Uecker
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Periodic Media ◽  
Nonlinear Schrödinger ◽  
Spatially Periodic

A remark about the justification of the nonlinear Schrödinger equation in quadratic spatially periodic media

2007 ◽  
Vol 59 (3) ◽  
pp. 554-557
Author(s):  
Carsten Blank ◽  
Martina Chirilus Bruckner ◽  
Christopher Chong ◽  
Vincent Lescarret ◽  
Guido Schneider ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Periodic Media ◽  
Nonlinear Schrödinger ◽  
Spatially Periodic

SUPER-RECURRENCE PHENOMENON RELEVANT TO THE PHASE IN THE NONLINEAR SCHRÖDINGER EQUATION

1995 ◽  
Vol 09 (17) ◽  
pp. 1045-1052 ◽  
Author(s):  
Y. YANG ◽  
Y. TAN ◽  
W.Y. ZHANG ◽  
C.Y. ZHENG
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Boundary Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Initial Condition ◽  
Nonlinear Schrödinger ◽  
Recurrence Period ◽  
Spatially Periodic ◽  
Good Agreement

The nonlinear Schrödinger equation with spatially periodic boundary conditions is numerically solved by means of the spectrum method. It is found that with the initial condition carefully chosen, the phase recurrence just appears when the amplitudes have the nineteenth recurrences to the initial condition. This phenomenon is called as the phase super-recurrence. Using a simple perturbation model, the amplitude recurrence period Ta and the phase change ∆φa in the period Ta are estimated, and a good agreement between this estimation and the numerical results of the nonlinear Schrödinger equation is shown.

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