Local regularity properties for 1D mixed nonlinear Schrödinger equations on half-line

doi:10.1007/s11464-020-0878-1

Front. Math. China

2020, Vol. 15

Issue (6) : 1121-1142 https://doi.org/10.1007/s11464-020-0878-1

RESEARCH ARTICLE

Local regularity properties for 1D mixed nonlinear Schrödinger equations on half-line

Boling GUO¹, Jun WU²(

)

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

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Abstract

The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrödinger equation $u t = i α u x x + β u 2 − u x + γ | u | 2 u x + i | u | 2 u$ on the half-line with inhomogeneous boundary condition. We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces. Moreover, we show that the nonlinear part of the solution on the half-line is smoother than the initial data.

Keywords Mixed nonlinear Schrödinger (MNLS) equations initial-boundary value problem (IBVP) Bourgain spaces local well-posedness

Corresponding Author(s): Jun WU

Issue Date: 05 February 2021

Cite this article:

Boling GUO,Jun WU. Local regularity properties for 1D mixed nonlinear Schrödinger equations on half-line[J]. Front. Math. China, 2020, 15(6): 1121-1142.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0878-1
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I6/1121

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