Nonlinear Subwavelength Resonances in Three Dimensions

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-03-16 DOI:10.1111/sapm.70036

Habib Ammari, Thea Kosche

引用次数: 0

Abstract

In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators with Kerr-type nonlinearities. Our discrete formulation is valid in both weak and strong nonlinear regimes. Compared to the linear formulation, it characterizes the extra experimentally observed eigenmodes that are induced by the nonlinearities.

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三维非线性亚波长共振

本文研究了三次非线性亥姆霍兹方程在亚波长区域的共振问题。我们导出了一个离散模型来近似具有克尔型非线性的高对比度谐振器有限系统的亚波长共振。我们的离散公式在弱和强非线性情况下都是有效的。与线性公式相比，它表征了由非线性引起的额外实验观察到的特征模态。

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

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.