Wave Equations of Macroscopic Generalized Electrodynamics

  • Eugene I. Nefyodov
  • Sergey M. Smolskiy
Part of the Textbooks in Telecommunication Engineering book series (TTE)


In Chap. 4 of our lecture course we shall become acquainted with the wave equations of macroscopic generalized electrodynamics (Sect. 4.1) and we show their distinctive features compared with the classic case (described in Chap. 3). The consequence of the Stokes–Helmholtz theorem (Sect. 1.3.1) about the fact that an electric field has the vortex and potential components is a significant feature of wave equation formation in generalized electrodynamics. This allows (as was done in Sect. 3.2) equations to obtained for the vector and scalar potentials. At this, the absence of a necessity to use the calibration relationships of Lorentz and Coulomb, respectively, is the essential feature. In this case, the one pair of wave equations obtained defines the transverse electromagnetic waves, whereas the second one defines the longitudinal waves.


  1. 12.
    Tomilin A.K. The Fundamentals of Generalized Electrodynamics.; Tomilin A.K. The Potential-Vortex Theory of the Electromagnetic Field (in English).
  2. 41.
    E.T. Whitteker. "A History of the Theories of Aether and Electricity" (From the Age of Descartes to the Close of the Nineteenth Century). LOGMANS, GREEN and Co., 39 PATERNOSTER ROW, LONDON, 1910. 502 P.Google Scholar
  3. 61.
    Kuzelev M.V., Rukhadze A.A. Electrodynamics of Dense Electron Beams in Plasma, English completed edition Plasma Free Electron Lasers Edition Frontier Paris. 1995.Google Scholar
  4. 5.
    Khvorostenko N.P. Longitudinal electromagnetic waves (in Russian)// Izvestia vuzov. Physics, 1992, № 3, p.24–29.Google Scholar
  5. 6.
    Nefyodov E.I., Subbotina T.I., Yashin A.A. Modern bioinformatics (in Russian).- Moscow: Telecom-Hot Line Publ., 2005.-272 p.Google Scholar
  6. 35.
    Sacco B., Tomilin A. The Study of Electromagnetic Processes in the Experiments of Tesla.
  7. 43.
    Nikolaev G.V. Electromagnetics Secrets and the free energy: new concepts of the physical world (in Russian). Tomsk. 2002.- 150 p.Google Scholar
  8. 44.
    Nikolaev G.V. Modern electrodynamics and reasons of its paradoxicality: prospect of consistent electrodynamics development (In Russian). Book 1.- Tomsk: Tverdynya Publ. 2003. -149 p.Google Scholar
  9. 8.
    Kasterin N.P. About wave propagation in heterogeneous medium. Part 1. Sound waves (in Russian). Moscow: University Publ., 1903.-165 p.Google Scholar
  10. 78.
    Kosterin N.P. Generalization of main equations of aerodynamics and electrodynamics (in Russian).- Moscow: AS USSR Publ., 1937.-21 p.Google Scholar
  11. 79.
    Mitkevich V.F. Physical action at a distance. Proceedings of the Russian Academy of Science. Series VII. Division of mathematical and natural science, 1391–1409 (1933).Google Scholar
  12. 55.
    Zhilin P.A. Reality and mechanics (in Russian) // Proceedings of XXIII school-seminar «Analysis and synthesis of non-linear mechanical oscillating systems», Sankt-Peterburg, 1-10 July, 1995. Institute of Machinery Problems Publ. 1996. Pp. 6–49.Google Scholar
  13. 81.
    van Vlaenderen K. J., Waser A. Generalization of classical electrodynamics to admit a scalar field and longitudinal waves// Hadronic Journal 24, 609–628 (2001).Google Scholar
  14. 82.
    Woodside D.A. Three-vector and scalar field identities and uniqueness theorems in Euclidean and Minkowski spaces// Am. J. Phys.,Vol.77, № 5, pp.438–446, 2009.Google Scholar
  15. 83.
    Arbab A. I., Satti Z. A. On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave// Progress in physics, 2009, v.2. – s. 8–13.Google Scholar
  16. 84.
    Podgainy D.V., Zaimidoroga O.A. Nonrelativistic theory of electroscalar field and Maxwell electrodynamics//
  17. 7.
    Tomilin A.K., Misiucenko L., Vikulin V.S. Relationships between Electromagnetic and Mechanical Characteristics of Electron // American Journal of Modern Physics and Application 2016; 3(1): pp.1–10.Google Scholar
  18. 88.
    Helmholtz H. About integrals of hydrodynamic equations, which correspond to the vortex motion. Crelles J. 55, 25 (1858).MathSciNetCrossRefGoogle Scholar
  19. 89.
    Rohrlich F. The dynamics of a charged sphere and the electron. American Journal of Physics 65 (11): pp.1051–1056 (1997). 1997,
  20. 90.
    Schwinger J. Electromagnetic mass revisited// Foundations of Physics, 13 (3): pp. 373–383, (1983).
  21. 91.
    Fedosin S. G. The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field. American Journal of Modern Physics. Vol. 3, №. 4, pp. 152–167 (2014).Google Scholar
  22. 92.
    Lorentz G.A. The theory of electrons and its application to the phenomena of light and heat radiation. Dover Publications, 2011, 352 p.Google Scholar
  23. 80.
    Kiryako A.G.: Theories of origin and generation of mass.
  24. 85.
    Stokes G. G. On some cases of fluid motion. Internet Archive. Transactions of the Cambridge Philosophical Society 8(1): 105–137(1843).Google Scholar
  25. 93.
    Kozyrev N.A. Selected works (in Russian). Leningrad University Publ., 1991.- 438 p.Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Eugene I. Nefyodov
    • 1
  • Sergey M. Smolskiy
    • 1
  1. 1.Durban Technological University (RSA)DurbanSouth Africa

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