Integrability and Dynamic Behavior of a Piezoelectro-Magnetic Circular Rod

Sarah M. Albalawi, Adel A. Elmandouh () and Mohammed Sobhy ()
Additional contact information
Sarah M. Albalawi: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Adel A. Elmandouh: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Mohammed Sobhy: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia

Mathematics, 2024, vol. 12, issue 2, 1-16

Abstract: The present work strives to explore some qualitative analysis for the governing equation describing the dynamic response of a piezoelectro-magnetic circular rod. As a result of the integrability study of the governed equation, which furnishes valuable insights into its structure, solutions, and applications in various fields, we apply the well-known Ablowitz–Ramani–Segur (ARS) algorithm to prove the non-integrability of the governed equation in a Painlevé sense. The qualitative theory for planar integrable systems is applied to study the bifurcation of the solutions based on the values of rod material properties. Some new solutions for the governing equation are presented and they are categorized into solitary and double periodic functions. We display a 3D representation of the solutions in addition to investigating the influence of wave velocity on the obtained solution for the particular material of the rod.

Keywords: bifurcation theory; phase portrait; soliton; piezoelectro-magnetic rod (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/2/236/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/2/236/ (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:12:y:2024:i:2:p:236-:d:1316981

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 ().