High-frequency two-dimensional asymptotic standing coastal trapped waves in nearly integrable case

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Vladislav Rykhlov, Anatoly Anikin
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引用次数: 0

Abstract

This paper continues the study of explicit asymptotic formulas for standing coastal trapped waves, focusing on the spectral properties of the operator \(\langle \nabla , D(x)\nabla \rangle \), which is the spatial component of the wave operator with a degenerating wave propagation velocity. We aim to construct spectral series—pairs of asymptotic eigenvalues and formal asymptotic eigenfunctions—corresponding to the high-frequency regime, where the eigenvalue is \(\varvec{\omega }\rightarrow \infty \). Extending earlier results, this study addresses the nearly integrable case, providing a more detailed asymptotic behavior of eigenfunctions. Depending on their domain of localization, these eigenfunctions can be expressed in terms of Airy functions and their derivatives or Bessel functions. In addition, we introduce a canonical operator with violated (imprecisely satisfied) quantization conditions.

Abstract Image

近可积情况下高频二维渐近驻岸困波
本文继续研究海岸驻波的显式渐近公式,重点研究了算子\(\langle \nabla , D(x)\nabla \rangle \)的频谱特性,它是波算子的空间分量,具有退化的波传播速度。我们的目标是构造与高频区域相对应的谱序列-渐近特征值对和形式渐近特征函数对,其中特征值为\(\varvec{\omega }\rightarrow \infty \)。本研究扩展了先前的结果,讨论了近可积情况,提供了特征函数的更详细的渐近行为。根据它们的定义域,这些特征函数可以用Airy函数及其导数或贝塞尔函数来表示。此外,我们还引入了一个违背(不精确满足)量化条件的正则算子。
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
Letters in Mathematical Physics
Letters in Mathematical Physics 物理-物理:数学物理
CiteScore
2.40
自引率
8.30%
发文量
111
审稿时长
3 months
期刊介绍: The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.
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