Global Solutions of Modified One-Dimensional Schrödinger Equation
Year: 2021
Author: Ting Zhang
Communications in Mathematical Research , Vol. 37 (2021), Iss. 3 : pp. 350–386
Abstract
In this paper, we consider the modified one-dimensional Schrödinger equation:
(Dt−F(D))u=λ|u|2u,
where F(ξ) is a second order constant coefficients classical elliptic symbol, and with smooth initial datum of size ε≪1. We prove that the solution is global-in-time, combining the vector fields method and a semiclassical analysis method introduced by Delort. Moreover, we get a one term asymptotic expansion for u when t→+∞.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0015
Communications in Mathematical Research , Vol. 37 (2021), Iss. 3 : pp. 350–386
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: Schrödinger equation semiclassical Analysis global solution.
Author Details
Ting Zhang Email
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