Open AccessWell-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation
Author(s) -
Boling Guo,
Jiangtao Wu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021205
Subject(s) - sobolev space , uniqueness , nonlinear system , mathematics , initial value problem , mathematical analysis , smoothing , boundary value problem , order (exchange) , nonlinear schrödinger equation , line (geometry) , property (philosophy) , schrödinger equation , physics , geometry , philosophy , statistics , finance , epistemology , quantum mechanics , economics
The main purpose of this paper is to study local regularity properties of the fourth-order nonlinear Schrödinger equations on the half line. We prove the local existence, uniqueness, and continuous dependence on initial data in low regularity Sobolev spaces. We also obtain the nonlinear smoothing property: the nonlinear part of the solution on the half line is smoother than the initial data.