scholarly journals On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation

2012 ◽  
Vol 5 (5) ◽  
pp. 971-987 ◽  
Author(s):  
Tetsu Mizumachi ◽  
◽  
Dmitry Pelinovsky ◽  
Keyword(s):  
Asymptotic Stability ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Localized Modes ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Nonlinear Schrödinger

scholarly journals ASYMPTOTIC STABILITY OF NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL

2005 ◽  
Vol 17 (10) ◽  
pp. 1143-1207 ◽  
Author(s):  
ZHOU GANG ◽  
I. M. SIGAL
Keyword(s):  
Asymptotic Stability ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Generalized Nonlinear Schrödinger Equation

We prove asymptotic stability of trapped solitons in the generalized nonlinear Schrödinger equation with a potential in dimension 1 and for even potential and even initial conditions.

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