A Method for Reducing Transcendental Dispersion Relations to Nonlinear Ordinary Differential Equations in a Wide Class of Wave Propagation Problems

Andrey Matskovskiy (), German Zavorokhin () and Pavel Petrov ()
Additional contact information
Andrey Matskovskiy: St. Petersburg Department of Steklov Mathematical Institute, Fontanka, 191023 St. Petersburg, Russia
German Zavorokhin: St. Petersburg Department of Steklov Mathematical Institute, Fontanka, 191023 St. Petersburg, Russia
Pavel Petrov: V.I. Il‘ichev Pacific Oceanological Institute, Baltiyskaya St., 690041 Vladivostok, Russia

Mathematics, 2022, vol. 10, issue 20, 1-11

Abstract: A class of problems of wave propagation in waveguides consisting of one or several layers that are characterized by linear variation of the squared refractive index along the normal to the interfaces between them is considered in this paper. In various problems arising in practical applications, it is necessary to efficiently solve the dispersion relations for such waveguides in order to compute horizontal wavenumbers for different frequencies. Such relations are transcendental equations written in terms of Airy functions, and their numerical solutions may require significant computational effort. A procedure that allows one to reduce a dispersion relation to an ordinary differential equation written in terms of elementary functions exclusively is proposed. The proposed technique is illustrated on two cases of waveguides with both compact and non-compact cross-sections. The developed reduction method can be used in applications such as geoacoustic inversion.

Keywords: underwater acoustics; diffraction; dispersion relation; special functions; nonlinear ordinary differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/20/3866/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/20/3866/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:20:p:3866-:d:946200

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().