Properties of an Operator Describing Acoustic Black Holes

IF 1.9 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI:10.1134/S1061920826020081

N.V. Ivanov, A.I. Shafarevich

引用次数: 0

Abstract

The properties of the operator describing flexural waves are described. This operator is defined by a fourth-order differential expression with a singular point. A Hilbert space is constructed, and the domain of the operator and the Gelfand triple are found. For a model operator corresponding to a quadratic profile, the spectrum and corresponding (distributional) eigenfunctions are explicitly calculated.

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描述声黑洞的算子的性质

描述了描述弯曲波的算子的性质。该算子由一个带奇异点的四阶微分表达式定义。构造了一个Hilbert空间，得到了算子的定义域和Gelfand三元组。对于对应于二次曲线的模型算子，明确地计算了谱和相应的（分布）特征函数。

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

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.