横向各向异性流形上非线性薛定谔方程线性化反边界值问题的稳定性增强

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-02-23 DOI:10.1088/1361-6420/ad2533

Shuai Lu, Jian Zhai

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引用次数: 0

摘要

我们考虑的问题是，在横向各向异性流形上，从线性化的狄利克特到诺伊曼映射中恢复非线性薛定谔方程中的非线性势函数。通过根据波长校准复几何光学解，我们证明了随着波长变大，恢复立方项系数的稳定性不断增强。

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Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds

We consider the problem of recovering a nonlinear potential function in a nonlinear Schrödinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex geometric optics solutions according to the wavenumber, we prove the increasing stability of recovering the coefficient of a cubic term as the wavenumber becomes large.

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.