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In this work, we investigate the dynamics of an uniaxial silica fiber under the viewpoint of propagation of ultimately ultrashort optical waveguide channels. As a result, we unveil the existence of three typical kinds of ultrabroadband excitations whose profiles strongly depend upon their angular momenta. Looking forward to surveying their scattering features, we unearth some underlying head-on scenarios of elastic collisions. Accordingly, we address some useful and straightforward applications in nonlinear optics through secured data transmission systems, as well as laser physics and soliton theory with optical soliton dynamics.

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.

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

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.