scholarly journals Quasi-Linear Dynamics in Nonlinear Schrödinger Equation with Periodic Boundary Conditions

2008 ◽  
Vol 281 (3) ◽  
pp. 655-673 ◽  
Author(s):  
M. Burak Erdoğan ◽  
Vadim Zharnitsky
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Linear Dynamics ◽  
Nonlinear Schrödinger

EXPECTED AND UNEXPECTED SOLUTIONS TO THE STATIONARY ONE-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1663-1667
Author(s):  
LINCOLN D. CARR ◽  
CHARLES W. CLARK ◽  
WILLIAM P. REINHARDT
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein Condensate ◽  
Dilute Gas

We present all stationary solutions to the nonlinear Schrödinger equation in one dimension for box and periodic boundary conditions. For both repulsive and attractive nonlinearity we find expected and unexpected solutions. Expected solutions are those that are in direct analogy with those of the linear Schödinger equation under the same boundary conditions. Unexpected solutions are those that have no such analogy. We give a physical interpretation for the unexpected solutions. We discuss the properties of all solution types and briefly relate them to experiments on the dilute-gas Bose-Einstein condensate.

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.

Sign in / Sign up

Export Citation Format

Share Document