scholarly journals Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Yong Chen ◽  
Zhenya Yan
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
Third Order Dispersion ◽  
Order Dispersion

scholarly journals Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Chachou Samet ◽  
M. Benarous ◽  
M. Asad-uz-zaman ◽  
U. Al Khawaja
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Cubic Nonlinearity ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
Third Order Dispersion ◽  
Solitonic Solution ◽  
Order Dispersion

We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities.

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