On a nonlinear Schrödinger equation with periodic potential

1999 ◽  
Vol 313 (1) ◽  
pp. 15-37 ◽  
Author(s):  
Thomas Bartsch ◽  
Yanheng Ding
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Potential ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

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.

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