In this work, we deal with the dynamics of a ferromagnet slab of zero conductivity under the influence of an external magnetic field and submitted to an electromagnetic wave perturbation as described by coupled complex-valued system equations. As a result, with the aid of the Painlevé analysis, we find that for the above ferrite system to support microwave excitations, the damping factor raised from the Landau–Lifshitz–Gilbert formalism ought to vanish while implying the existence of some set of infinite law of conservations. Following the underlying feature of Kruskal’s approach to generating in a straightforward manner some typical solutions, we henceforth discuss the physical implications of the traveling waveguide excitations.

In this work, we delve into the structure of some typical microwave ferrites while investigating the propagation of nonlinear circularly polarized waveguide excitations. In the standpoint, we consider a ferromagnetic slab insulator of 0.5 mm thickness submitted to an external transverse magnetic field.Combining the Landau-Lifshitz-Gilbert formalism of evolution of the magnetization to Maxwell equations, we survey the interaction process of an electromagnetic wave perturbation with the slab. As a result, using the perturbative scaling approach suitable to high-frequency excitations, we derive some new evolution system describing the propagation of circularly polarized waves in the medium. Pursuing further with the analysis, we unwrap the integrability properties of the new system using the singularity structure method where sufficient arbitrary functions are generated. Taking advantage of such properties, we construct a rich variety of nonlinear excitations, solutions to the ferrite dynamics. Additionally, we address some physical implications of the results obtained previously.

In this work, we investigate fractals in arrays of carbon nanotubes modeled by an evolution equation derived by using a rigorous application of the reductive perturbation formalism for the Maxwell equations and for the corresponding Boltzmann kinetic equation of the distribution function of electrons in such nanomaterials. We study the integrability properties of our dynamical system by using the Weiss-Tabor-Carnevale analysis. Actually, following the leading order analysis, we write the solution in the form of series of Laurent. We also use the Kruskal's simplification to find the solutions. Using the truncated Painlevé expansion, we construct the auto-Backlund transformation of the system. We take advantage of the above properties to construct a wide panel of structures with fractals properties. As a result, we unearth some typical features, namely the fractal dromion, the fractal lump, the stochastic and nonlocal fractal excitations. We also address some physical implications of the results obtained.

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