Influence of internal magnetic field on magnetization in ferromagnetic materials via Kraenkel-Manna-Merle system: dual-wave patterns, sensitivity and stability analysis

In this study, it is shown that in the Kraenkel-Manna-Merle system (KMMS) an internal magnetic field (IMF) can be generated. This is achieved mathematically as the equation that describes the external magnetic field is integrable. An evolutionary system can generate an internal source by introducing the "duality transformation" which leads to creating "dual waves". Alongside a non-autonomous KMMS is considered, that describes nonuniform magnetic field formation. The system's exact solutions are found using the extended unified method. Various wave patterns are revealed, fission-fusion graded solitons, braided solitons, envelope solitons, zig-zag cliff wave shape, lump vector, zig-zag cavity solitons. and upper and lower saucers with surface-based lattices. The most revealed interesting phenomenon is the localization of the magnetic field created in FMMs, which agrees with the experimental work. The sensitivity of the system is tested against the IMF and also, against a perturbation in the external magnetic field. It is remarked that the intensity of the magnetic field, created in ferromagnetic materials, is highly exceeding that one of the external magnetic field amplitude. That is, magnetization by time varying magnetic field is highly efficient.