Asymptotics for the third-order nonlinear Schrödinger equation in the critical case

2016 ◽  
Vol 40 (5) ◽  
pp. 1573-1597 ◽  
Author(s):  
Nakao Hayashi ◽  
Elena I. Kaikina
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Critical Case ◽  
Nonlinear Schrodinger Equation ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
The Third

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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