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Article

  • Title

    Detailed explicit solution of the electrodynamic wave equations

  • Authors

    Dmitrieva Iryna Yu.

  • Subject

    ELECTRONICS. RADIO ENGINEERING. TELECOMMUNICATION FACILITIES

  • Year 2015
    Issue 2(46)
    UDC 621.371+537.8:621.372
    DOI 10.15276/opu.2.46.2015.26
    Pages 145-154
  • Abstract

    Present results concern the general scientific tendency dealing with mathematical modeling and analytical study of electromagnetic field phenomena described by the systems of partial differential equations. Specific electrodynamic engineering process with expofunctional influences is simulated by the differential Maxwell system whose effective research is equivalent to the rigorous solution of the general wave partial differential equation regarding all scalar components of electromagnetic field vector intensities. The given equation is solved explicitly in detail using method of integral transforms and irrespectively to the concrete boundary conditions. Specific cases of unexcited vacuum and isotropic homogeneous medium were considered. Proposed approach can be applied to any finite dimensional system of partial differential equations with piece wise constant coefficients and its corresponding scalar equations representing mathematical models in modern electrodynamics. In comparison with the known results, current research is completely thorough and accurate that implies its direct practical application.

  • Keywords

    differential Maxwell system, general wave equation regarding all scalar components of electromagnetic field vector intensities, detailed explicit solution

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  • References

    Література
    1.    Dmitrieva, I.Yu. Diagonalization of the differential operator matrix in the case of the multidimensional circuits / I.Yu. Dmitrieva, A.M. Ivanitckiy // Наукові праці ОНАЗ ім. О.С. Попова. — 2009. — № 1. — С. 36—51.
    2.    Dmitrieva, I. Some cases of electromagnetic wave propagation in terms of analytical study / I. Dmitrieva // Proceedings of the International Symposium on Signals, Circuits and Systems (ISSCS’2013), July 11–12, 2013, Iasi, Romania. — Piscataway, NJ: IEEE, 2013. — PP. 1—4.
    3.    Dmitrieva, I. On the solution of some differential equation in the classical Maxwell theory / I. Dmitrieva // Hyperion International Journal of Econophysics & New Economy. — 2009. — Vol. 2, Issue 2. — PP. 151—164.
    4.    Tranter, C.J. Integral Transforms in Mathematical Physics / C.J. Tranter. — 2nd Ed. — London: Methuen; New York: Wiley, 1956. — 133 p.
    5.    Камке, Э. Справочник по обыкновенным дифференциальным уравнениям / Э. Камке; пер. С.В. Фомин. — 5-е изд., стер. — М.: Наука, 1976. — 576 с.

    References
    1.    Dmitrieva, I.Yu. and Ivanitckiy, A.M. (2009). Diagonalization of the differential operator matrix in the case of the multidimensional circuits. Proceedings of the O.S. Popov ОNAT, 1, 36—51.
    2.    Dmitrieva, I. (2013). Some cases of electromagnetic wave propagation in terms of analytical study. In Proceedings of the International Symposium on Signals, Circuits and Systems (ISSCS’2013) (pp. 1—4). Piscataway, NJ: IEEE.
    3.    Dmitrieva, I. (2009). On the solution of some differential equation in the classical Maxwell theory. Hyperion International Journal of Econophysics & New Economy, 2(2), 151—164.
    4.    Tranter, C.J. (1956). Integral Transforms in Mathematical Physics (2nd Ed.). London: Methuen; New York: Wiley.
    5.    Kamke, E. (1965-1967). Differentialgleichungen. Lösungsmethoden und Lösungen (Vols. 1-2). Akademische Verlagsgesellschaft.

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