Quasiclassical scattering of wave packets on a narrow band in which the potential rapidly changes
type: Item
instance of: scholarly article
title: Quasiclassical scattering of wave packets on a narrow band in which the potential rapidly changes
zbMATH Open document ID: 0689.35080
DOI: 10.1007/BF01158720
published in: Mathematical Notes
publication date: 1989-01-01T00:00:00Z
review text: Let \(\psi\) satisfy an equation \[ i\hslash \partial \psi /\partial t=- \hslash^ 2\Delta \psi +| \nabla \Phi |^ 2V(\Phi (x)/\hslash)\psi +V_ 0(x)\psi,x\in {\mathbb{R}}, \] and an initial condition \[ H_{t=0}=\phi_ 0(x) \exp (i\hslash^{-1}S(x)), \] where functions \(\phi_ 0,S_ 0,\Phi,V_ 0\) and V are given. The asymptotics of \(\psi\) (x,t,\(\hslash)\) as \(\hslash \to 0\) and \(t\in [0,T]\) with fixed T is found.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 4129335
zbMATH Keywords: classical limit
zbMATH Keywords: nonlinear Schrödinger equation
author: A. I. Shafarevich
reviewed by: Dmitri Yafaev
MaRDI profile type: Publication
cites work: Q4040558
cites work: Q3896271
cites work: Q3344582
cites work: Q3317424
cites work: Q3732103
cites work: Q3896270
description: scientific article; zbMATH DE number 4129335