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:
$$(D_t-F(D))u=λ|u|^2u,$$
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 $t→+∞$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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
-
Modified Scattering for the One-Dimensional Schrödinger Equation with a Subcritical Dissipative Nonlinearity
Liu, Xuan | Zhang, TingJournal of Dynamics and Differential Equations, Vol. 37 (2025), Iss. 1 P.577
https://doi.org/10.1007/s10884-023-10272-4 [Citations: 1] -
Global existence and asymptotics for the modified two-dimensional Schrödinger equation in the critical regime
Liu, Xuan | Zhang, TingNonlinearity, Vol. 36 (2023), Iss. 12 P.6324
https://doi.org/10.1088/1361-6544/ad027b [Citations: 0]