Coordinate asymptotic behavior of the solution of the scattering problem for the Schr�dinger equation

1974 ◽  
Vol 19 (2) ◽  
pp. 465-476 ◽  
Author(s):  
V. S. Buslaev ◽  
M. M. Skriganov
Keyword(s):  
Asymptotic Behavior ◽  
Scattering Problem ◽  
Dinger Equation

scholarly journals Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation

2021 ◽  
pp. 1-24
Author(s):  
Dario Benedetto ◽  
Emanuele Caglioti ◽  
Stefano Rossi
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Scattering Problem ◽  
New Method ◽  
Landau Damping ◽  
The Cauchy Problem ◽  
The One ◽  
Perturbative Result

We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this “scattering problem”, closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.

scholarly journals Scattering Problem for the Supercritical Nonlinear Schrödinger Equation in 1d

2015 ◽  
Vol 58 (3) ◽  
pp. 451-470
Author(s):  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Scattering Problem ◽  
Dinger Equation

scholarly journals Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Lung-Hui Chen
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Scattering Theory ◽  
Complex Analysis ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattered Wave ◽  
Phase Information ◽  
Wave Fields ◽  
Inverse Scattering Theory

We consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. In some micro/nanostructures, it is impractical to measure the phase information of the scattered wave field emitted from the source. We study the asymptotic behavior of the scattering amplitudes/intensity from the linearization theory of the scattered wave fields. The inverse uniqueness of the scattered waves is reduced to the inverse uniqueness of the analytic function. We deduce the uniqueness of the Schrödinger potential via the identity theorems in complex analysis.

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