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Zig-zag, bright, short and long solitons formation in inhomogeneous ferromagnetic materials.Kraenkel-Manna-Merle equation with space dependent coefficients

The ferromagnetism induced by an external magnetic field (EMF), in (3+1) dimensions, is governed by Kraenkel–Manna–Merle equation (KMME). A (1+1) dimensionalmodel equation was derived in the literature. Here, this later model equation is considered with space-dependent coefficients, which stands to inhomogeneous ferromagnetism. Exact solutions are obtained by using the extended unified method. The numerical results of the solutions are represented in graphs. They show multiple geometric waves structures, which are zig-zag bright, short and long, solitons in ferromagnetic materials (FMMs). It is found that when the EMF exhibits short (or ultra short), the ferromagnitization exhibits long (or short) solitons. It is also observed that that the ferromagnetism exhibits highly oscillatory waves, with increasing damping parameter. The novelty of this work stems from the fact that the problem of in-homogeneous ferromagentism, studied here is completely new. Further, the zig-zag solitons structures, found here, are so.