@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 = {<p style="text-align: justify;">In this paper, we consider the modified one-dimensional Schrödinger equation:<br/>$$(D_t-F(D))u=λ|u|^2u,$$</p><p style="text-align: justify;">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 $u$&nbsp;when $t→+∞$.<br/></p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2021-0015},
url = {http://global-sci.org/intro/article_detail/cmr/19265.html}
}