Effect of the Third-Order Dispersion on the Nonlinear Schrödinger Equation

1993 ◽  
Vol 62 (7) ◽  
pp. 2324-2333 ◽  
Author(s):  
Masayuki Oikawa
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
The Third ◽  
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.

On well-posedness of the third-order nonlinear Schrödinger equation with time-dependent coefficients

2015 ◽  
Vol 17 (04) ◽  
pp. 1450031 ◽  
Author(s):  
Xavier Carvajal ◽  
Mahendra Panthee ◽  
Marcia Scialom
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scaling Limit ◽  
Nonlinear Schrodinger Equation ◽  
Time Dependent ◽  
Well Posedness ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
The Third

We consider the Cauchy problem associated to the third-order nonlinear Schrödinger equation with time-dependent coefficients. Depending on the nature of the coefficients, we prove local as well as global well-posedness results for given data in L2-based Sobolev spaces. We also address the scaling limit to fast dispersion management and prove that it converges in H1to the solution of the averaged equation.

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