Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation

Boling Guo; Jun Wu

doi:10.3934/dcdsb.2021205

Article Contents

2022, Volume 27, Issue 7: 3749-3778. Doi: 10.3934/dcdsb.2021205

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Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation

Boling Guo^1, and
Jun Wu^2, ,

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
^* Corresponding author: Jun Wu

Received: February 2021

Revised: June 2021

Early access: August 2021

Published: July 2022

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Abstract

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.

Keywords:

Fourth-order nonlinear Schrödinger equations,
initial-boundary value problem,
local well-posedness,
nonlinear smoothing.

Mathematics Subject Classification: Primary: 35Q55, 35G31; Secondary: 35M10.

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References

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