Application of Argument Principle for Study a Structure of Roots of Transcendental Equations

Subscription Access

Authors

  • Nail Suleiman Khabeev Department of Mathematics, University of Bahrain, Kingdom of Bahrain Author

DOI:

https://doi.org/10.5890/JVTSD.2021.09.003

Abstract

In study of the structure of shock waves in bubbly liquids we need to find integral curve connecting two singular points of the system of differential equations. We linearized the system of basic equations around equilibrium state. The condition of existence of nontrivial solution of the linear equations leads to the characteristic transcendental equation with respect to exponential index. The structure of roots of such equation is studied by using argument principle [1]. It is shown that for compression waves such equation has one real root.

References

[1] Mathews, J.M. and Howell, R.W. (2006), Complex Analysis for Mathematics and Engineering, Jones and Bartlett, London.

[2] Shagapov, V.S., Gimaltdinov, I.K., Khabeev, N.S., and Bailey, S.S. (2003), Acoustic Waves in a Liquid with a Bubble Screen, Shock waves, 13(1), 49-56.

[3] Nigmatulin, R.I., Khabeev, N.S., and Hai, Z.N. (1988), Waves in Liquids with Vapour Bubbles, Journal of fluid mechanics, 185, 85-117.

Downloads

Article Metrics

Citations 0 Crossref
PublishedSeptember 2021

Usage tracking begins September 1, 2026.

History Published

Issue

Vol. 5 No. 3 (2021): Regular Issue

Section

Research Articles

License

Unless an article landing page states a Creative Commons or other article-specific license, the article is published by L&H Scientific Publishing, LLC and all rights are reserved. The article-level license and copyright notice govern access and reuse.

How to Cite

Khabeev, N. S. (2026). Application of Argument Principle for Study a Structure of Roots of Transcendental Equations. Journal of Vibration Testing and System Dynamics, 5(3), 233-236. https://doi.org/10.5890/JVTSD.2021.09.003

Share

Tweet Share