Energy critical Schrödinger equation with weighted exponential nonlinearity: Local and global well-posedness

2018 ◽  
Vol 15 (04) ◽  
pp. 599-621
Author(s):  
Abdelwahab Bensouilah ◽  
Dhouha Draouil ◽  
Mohamed Majdoub
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Well Posedness ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Nonlinear Schrödinger

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with weighted exponential nonlinearity [Formula: see text] where [Formula: see text] and [Formula: see text]. We establish local and global well-posedness in the subcritical and critical regimes.

L∞C(ℝn)-decay of classical solutions for nonlinear Schrödinger equations

1986 ◽  
Vol 104 (3-4) ◽  
pp. 309-327 ◽  
Author(s):  
Nakao Hayashi ◽  
Masayoshi Tsutsumi
Keyword(s):  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Classical Solutions ◽  
Initial Value ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Sign Conditions ◽  
Image Position

SynopsisWe study the initial value problem for the nonlinear Schrödinger equationUnder suitable regularity assumptions on f and ø and growth and sign conditions on f, it is shown that the maximum norms of solutions to (*) decay as t→² ∞ at the same rate as that of solutions to the free Schrödinger equation.

scholarly journals Numerical Optics Soliton Solution of the Nonlinear Schrödinger Equation Using the Laplace and the Modified Laplace Decomposition Method

2019 ◽  
pp. 1-13
Author(s):  
M. M. El-Horbaty ◽  
F. M. Ahmed
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Initial Value ◽  
Nonlinear Schrödinger ◽  
Laplace Decomposition Method

In this paper, the Laplace decomposition method (LDM) and some modification, namely the Modified Laplace decomposition method (MLDM), are adopted to numerically investigate the optic soliton solution of the nonlinear complex Schrödinger equation (NLSE). The obtained results demonstrate the reliability and the efficiency of the considered methods to numerically approximate such initial value problems (IVPs).

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