Abstract
We investigate throughout this paper the effect of inhomogeneity on the propagation of solitons in ferromagnetic systems governing the magnetization evolution in a magnetic medium. Indeed we focus our attention on a nonlinear evolution equation derived by M. Saravanan and A. Arnaudon (2018 Phys. Lett. A 382 2638) that takes into account the inhomogeneity we are interested in. The perturbed soliton solutions are constructed using a multiple scale soliton perturbation theory by solving the associated linear eigenvalue problem with proper derivation of complete set of eigenfunctions. We present two types of inhomogeneities, such as localized and linear, and their effects on soliton propagation. It is found that the localized inhomogeneity supports stable soliton excitations with constant amplitude.
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