scholarly journals Beyond Nonlinear Schrödinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interactions

2001 ◽  
Vol 8 (sup1) ◽  
pp. 139-144 ◽  
Author(s):  
D Grecu ◽  
Anca Vis¸inescu ◽  
A S Cârstea
Keyword(s):  
Schrödinger Equation ◽  
Long Range ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Long Range Interactions

scholarly journals Pattern formation in the nonlinear Schrödinger equation with competing nonlocal nonlinearities

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
F. Maucher ◽  
T. Pohl ◽  
W. Krolikowski ◽  
S. Skupin
Keyword(s):  
Schrödinger Equation ◽  
Long Range ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Beam Propagation ◽  
Nonlinear Schrodinger Equation ◽  
Stable States ◽  
Nonlinear Schrödinger ◽  
Long Range Ordering ◽  
Nonlocal Nonlinearities

AbstractWe study beam propagation in the framework of the nonlinear Schrödinger equation with competing Gaussian nonlocal nonlinearities. We demonstrate that such system can give rise to self-organization of light into stable states of trains or hexagonal arrays of filaments, depending on the transverse dimensionality. This long-range ordering can be achieved by mere unidirectional beam propagation. We discuss the dynamics of long-range ordering and the crucial role which the phase of the wavefunction plays for this phenomenon. Furthermore we discuss how transverse dimensionality affects the order of the phasetransition.

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