scholarly journals Large time behavior in nonlinear Schrödinger equations with time dependent potential

2015 ◽  
Vol 13 (2) ◽  
pp. 443-460 ◽  
Author(s):  
Rémi Carles ◽  
Jorge Drumond Silva
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Nonlinear Schrödinger Equations ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Time Behavior ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Dependent Potential

scholarly journals SHARP ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO NONLINEAR SCHRÖDINGER EQUATIONS WITH REPULSIVE INTERACTIONS

2005 ◽  
Vol 07 (02) ◽  
pp. 167-176 ◽  
Author(s):  
NAOYASU KITA ◽  
TOHRU OZAWA
Keyword(s):  
Large Time Behavior ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Repulsive Interactions ◽  
The Cauchy Problem

A detailed description is given on the large time behavior of scattering solutions to the Cauchy problem for nonlinear Schrödinger equations with repulsive interactions in the short-range case without smallness condition on the data.

Short Time Behavior of Solutions to Linear and Nonlinear Schrödinger Equations

2008 ◽  
Vol 60 (5) ◽  
pp. 1168-1200 ◽  
Author(s):  
Michael Taylor
Keyword(s):  
Broad Class ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Time Behavior ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Pinsky Phenomenon ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear ◽  
Short Time

AbstractWe examine the fine structure of the short time behavior of solutions to various linear and nonlinear Schrödinger equations ut = iΔu+q(u) on I×ℝn, with initial data u(0, x) = f (x). Particular attention is paid to cases where f is piecewise smooth, with jump across an (n−1)-dimensional surface. We give detailed analyses of Gibbs-like phenomena and also focusing effects, including analogues of the Pinsky phenomenon. We give results for general n in the linear case. We also have detailed analyses for a broad class of nonlinear equations when n = 1 and 2, with emphasis on the analysis of the first order correction to the solution of the corresponding linear equation. This work complements estimates on the error in this approximation.

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