@Article{CMR-37-350,
author = {Zhang , Ting},
title = {Global Solutions of Modified One-Dimensional Schrödinger Equation},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {37},
number = {3},
pages = {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 $t→+∞$.
},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2021-0015},
url = {http://global-sci.org/intro/article_detail/cmr/19265.html}
}
TY - JOUR
T1 - Global Solutions of Modified One-Dimensional Schrödinger Equation
AU - Zhang , Ting
JO - Communications in Mathematical Research
VL - 3
SP - 350
EP - 386
PY - 2021
DA - 2021/06
SN - 37
DO - http://doi.org/10.4208/cmr.2021-0015
UR - https://global-sci.org/intro/article_detail/cmr/19265.html
KW - Schrödinger equation, semiclassical Analysis, global solution.
AB -
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 $t→+∞$.
Ting Zhang. (2021). Global Solutions of Modified One-Dimensional Schrödinger Equation.
Communications in Mathematical Research . 37 (3).
350-386.
doi:10.4208/cmr.2021-0015
