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Kinks and Maxwell's Equations--EM Wave Radiation

In some more advanced physics books, the idea of how waves form and detach from an oscillating electric dipole is shown using the concept of a kink. Is it possible to derive the propagated wave equation from that approach, or does it simply require Maxwell's equations?

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              Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
                  (121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
                   Obz Site:  39° 15' 7" N, 121° 2' 32" W, 2700 feet

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