Euler–Darboux–Poisson Equation in Context of the Traveling Waves in a Strongly Inhomogeneous Media

Ioann Melnikov () and Efim Pelinovsky ()
Additional contact information
Ioann Melnikov: Faculty of Informatics, Mathematics and Computer Science, HSE University, Nizhny Novgorod 603155, Russia
Efim Pelinovsky: Faculty of Informatics, Mathematics and Computer Science, HSE University, Nizhny Novgorod 603155, Russia

Mathematics, 2023, vol. 11, issue 15, 1-12

Abstract: The existence of traveling waves in an inhomogeneous medium is a vital problem, the solution of which can help in modeling the wave propagation over long distances. Such waves can be storm waves or tsunami waves in the seas and oceans. The presence of solutions in the form of traveling waves indicates that the wave propagates without reflection and, therefore, can transfer energy over long distances. Traveling waves within the framework of the 1D variable-coefficient wave equation exist only for certain configurations of an inhomogeneous medium, some of which can be found by transforming the original equation to the Euler–Darboux–Poisson equation. The solution of the last equation for certain parameter values is expressed in elementary functions, which are the sum of waves running in opposite directions. The mathematical features of such a transformation are discussed in this paper.

Keywords: Euler–Darboux–Poisson equation; traveling waves; inhomogeneous media; wave equation; shallow sea (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/15/3309/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/15/3309/ (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:11:y:2023:i:15:p:3309-:d:1204354

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 ().