Increasing Stability of the First Order Linearized Inverse Schrödinger Potential Problem with Integer Power Type Nonlinearities

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-08-22 DOI:10.1137/22m1542817

Sen Zou, Shuai Lu, Boxi Xu

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1868-1889, August 2024.
Abstract. We investigate the increasing stability of the inverse Schrödinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized problem with respect to the unknown potential function, a combination formula of the first order linearization is proposed, which provides a Lipschitz type stability for the recovery of the Fourier coefficients of the unknown potential function in low frequency mode. These stability results highlight the advantage of nonlinearity in solving this inverse potential problem by explicitly quantifying the dependence on the wavenumber and the nonlinearity index. A reconstruction algorithm for integer power type nonlinearities is also provided. Several numerical examples illuminate the efficiency of our proposed algorithm.

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具有整数幂型非线性的一阶线性化反薛定谔势问题的稳定性提升

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1868-1889 页，2024 年 8 月。摘要。我们研究了具有整数幂型非线性的反薛定谔势问题在大波数下的增大稳定性。通过考虑关于未知势函数的一阶线性化问题，提出了一阶线性化的组合公式，该公式为在低频模式下恢复未知势函数的傅里叶系数提供了 Lipschitz 型稳定性。这些稳定性结果通过明确量化对波长和非线性指数的依赖，突出了非线性在解决反电势问题中的优势。此外，还提供了整数功率型非线性的重构算法。几个数值示例说明了我们提出的算法的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.