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Hamiltonian Form of the Maxwell Equations and Its Generalized Solutions

Hamiltonian Form of the Maxwell Equations and Its Generalized Solutions Differential Equations, Vol. 39, No. 6, 2003, pp. 807–816. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 6, 2003, pp. 769–776. Original Russian Text Copyright c 2003 by Alekseeva. PARTIAL DIFFERENTIAL EQUATIONS Hamiltonian Form of the Maxwell Equations and Its Generalized Solutions L. A. Alekseeva Institute for Mathematics, National Academy of Sciences, Almaty, Kazakhstan Received July 1, 2001 The Maxwell equations describing electromagnetic waves are symmetric under the interchange of the electric and magnetic elds E and H . This fact, well known in electrodynamics, is helpful in the construction of solutions. One can often use solutions of boundary value problems for electric elds to obtain solutions of similar problems for magnetic elds and vice versa merely by the substitution E H accompanied by the interchange "  of permittivity and permeability. Only the condition that there are no magnetic charges and, accordingly, magnetic currents violates the symmetry. Here we drop this condition and construct a single complex di erential equation for a complex three-dimensional vector A- eld, which is equivalent to the system of Maxwell equations in the presence of electric and magnetic charges and currents. To analyze this equation, referred to as the Hamiltonian form of the Maxwell http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Hamiltonian Form of the Maxwell Equations and Its Generalized Solutions

Alekseeva, L.
Differential Equations , Volume 39 (6) – Oct 5, 2004
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References (1)

Publisher
Springer Journals
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/B:DIEQ.0000008408.67161.19
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 39, No. 6, 2003, pp. 807–816. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 6, 2003, pp. 769–776. Original Russian Text Copyright c 2003 by Alekseeva. PARTIAL DIFFERENTIAL EQUATIONS Hamiltonian Form of the Maxwell Equations and Its Generalized Solutions L. A. Alekseeva Institute for Mathematics, National Academy of Sciences, Almaty, Kazakhstan Received July 1, 2001 The Maxwell equations describing electromagnetic waves are symmetric under the interchange of the electric and magnetic elds E and H . This fact, well known in electrodynamics, is helpful in the construction of solutions. One can often use solutions of boundary value problems for electric elds to obtain solutions of similar problems for magnetic elds and vice versa merely by the substitution E H accompanied by the interchange "  of permittivity and permeability. Only the condition that there are no magnetic charges and, accordingly, magnetic currents violates the symmetry. Here we drop this condition and construct a single complex di erential equation for a complex three-dimensional vector A- eld, which is equivalent to the system of Maxwell equations in the presence of electric and magnetic charges and currents. To analyze this equation, referred to as the Hamiltonian form of the Maxwell

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Differential Equations – Springer Journals

Published: Oct 5, 2004

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