The perturbational stability of the Schr$\ddot{o}$dinger equation
Analysis of PDEs
2020-09-22 v1
Abstract
By using the Wigner transform, it is shown that the nonlinear Schrdinger equation can be described, in phase space, by a kinetic theory similar to the Vlasov equation which is used for describing a classical collisionless plasma. In this paper we mainly show Landau damping in the quantum sense, namely,quantum Landau damping exists for the Wigner-Poisson system. At the same time, we also prove the existence and the stability of the nonlinear Schrdinger equation under the quantum stability assumption.
Keywords
Cite
@article{arxiv.2009.09855,
title = {The perturbational stability of the Schr$\ddot{o}$dinger equation},
author = {Xixia Ma},
journal= {arXiv preprint arXiv:2009.09855},
year = {2020}
}
Comments
21pages. arXiv admin note: text overlap with arXiv:1810.10955, arXiv:1807.05254; text overlap with arXiv:quant-ph/0505004 by other authors