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Abstract: The complex form of Maxwell equations has been constructed as one equationfor 3-dimensional complex A-vector. The real and imaginary parts of this vectorare described with use of electric and magnetic tensions accordingly. Withusing a theory of generalized functions for new equations, the strong shockelectro-magnetic waves with the gap of tensions on fronts are considered. Theconditions on wave fronts have been received. It-s shown that gap of thetensions is tangent to the front of a wave, i.e. shock electromagnetic wavesare transverse and charges on the front of wave are absent. Generalized laws ofconservation of energy and charges have been received including ones on thefronts of shock waves. The generalized solutions of this equations and solutionof Caushy problem have been constructed and the theorems of their uniquenesshave been proved including the shock waves.



Author: Lyudmila A. Alexeyeva

Source: https://arxiv.org/







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