The complexity of wave propagation of the nonlinear Schrödinger equation with weak periodic external field

2008 ◽  
Vol 68 (2) ◽  
pp. 420-429
Author(s):  
Yanxia Hu ◽  
Keying Guan
Keyword(s):  
Wave Propagation ◽  
External Field ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Periodic External Field

Seesaw drift of bright solitons of the nonlinear Schrödinger equation with a periodic potential

2016 ◽  
Vol 25 (03) ◽  
pp. 1650038 ◽  
Author(s):  
Camilo J. Castro ◽  
Deterlino Urzagasti
Keyword(s):  
External Field ◽  
Schrödinger Equation ◽  
Fiber Optics ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Potential ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Analytical Approximations

Soliton solutions are investigated employing the nonlinear Schrödinger equation (NLSE) with an additional term corresponding to an external periodic field. In particular, we use this equation to describe the behavior of solitons in fiber optics in the case of anomalous dispersion. Employing the framework of variational analysis and analytical approximations, single peaked soliton solutions are derived, which exhibit variations of the solitonic parameters due to the effect of the periodic potential and a harmonic oscillator motion of the soliton center, when the frequency of the external field is small, whereas high values of the frequency of the external field produce static solitons. Finally, a variational-numerical analysis was developed and compared with a purely numerical model.

scholarly journals MATTER WAVE PROPAGATION ABOVE A STEP POTENTIAL WITHIN THE CUBIC-NONLINEAR SCHRÖDINGER EQUATION

2012 ◽  
Vol 15 ◽  
pp. 232-239
Author(s):  
HAYK ISHKHANYAN ◽  
ASHOT MANUKYAN ◽  
ARTUR ISHKHANYAN
Keyword(s):  
Wave Propagation ◽  
Schrödinger Equation ◽  
Elliptic Curve ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Matter Wave ◽  
Step Potential ◽  
Nonlinear Schrödinger ◽  
Cubic Nonlinear Schrödinger Equation

We analyze the matter wave transmission above a step potential within the framework of the cubic-nonlinear Schrödinger equation. We present a comprehensive analysis of the corresponding stationary problem based on an exact second-order nonlinear differential equation for the probability density. The exact solution of the problem in terms of the Jacobi elliptic sn-function is presented and analyzed. Qualitatively distinct types of wave propagation picture are classified depending on the input parameters of the system. Analyzing the 2D space of involved dimensionless parameters, the nonlinearity and the reflecting potential's height/depth given in the units of the chemical potential, we show that the region of the parameters that does not sustain restricted solutions is given by a closed curve consisting of a segment of an elliptic curve and two line intervals. We show that there exists a specific singular point, belonging to the elliptic curve, which causes a jump from one evolution scenario to another one. The position of this point is determined and the peculiarities of the evolution scenarios (oscillatory, non-oscillatory and diverging) for all the allowed regions of involved parameters are described and analyzed in detail.

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