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We study the conditions for a wave-like solution in the context of an electromagnetic field diffusing into nonlinear magnetic conducting media. In the usual B-H relation, the differential magnetic permeability has only positive values. Through an analytical treatment, we show that it is possible to find an attenuation less field behavior inside media with an appropriate induction (B) and magnetic field (H) relation, under the assumption that the differential magnetic permeability can also assume negative values. The wave-like solution leads to unusual electromagnetic behavior and invites further investigation into practical applications.