Alfvén waves (AWs) are classified as low-frequency transverse electromagnetic waves that propagate along the lines of the magnetic field (MF). These waves can be generated in electrically conducting fluids, such as plasma.
Alfvén waves are a type of plasma wave that occur in magnetized plasmas, where ions oscillate due to the tension in magnetic field lines. They play a crucial role in various astrophysical phenomena, including energy transport in the solar atmosphere and particle acceleration.

The characteristics of small-amplitude kinetic Alfvén waves (KAWs) in a typical magnetoplasma, where both ions and electrons are considered to have a regularized kappa distribution (RKD). The restrictions imposed on the standard Kappa distribution function will be removed by considering the RKD function. The RKD can also be used for kappa areas for spectral index κ < 3/2. We then use the Korteweg–de Vries equation to investigate the KAWs in this model, which we obtained from the reductive perturbation method. It is observed that the equation’s nonlinear and dispersive coefficients are functions of the Kummar functions and the cut-off parameter. It is found that the nonlinear and dispersive coefficients of this equation depend on the Kummar functions and the cut-off parameter. Due to the negativity of the coefficients of the wave equation, only compressive KAWs can exist and propagate in this model. The numerical results demonstrate a positive correlation between the soliton’s profile (amplitude and width) with an increase in the cut-off parameter. Conversely, the superthermality has a negative influence on the soliton profile. The influence of the soliton’s propagation angle on the magnetic field’s direction is investigated. It is found that the solitary wave will not propagate in the ambient when the propagation angle θ becomes 0 or 90. Overall, the results obtained from this research can be used in space and laboratory plasmas with low β that have non-Maxwellian electrons.