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doi: 10.3934/dcdsb.2021205
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## Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation

 1 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China 2 Graduate School of China Academy of Engineering Physics, Beijing 100088, China

* Corresponding author: Jun Wu

Received  February 2021 Revised  June 2021 Early access August 2021

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.

Citation: Boling Guo, Jun Wu. Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021205
##### References:

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