Analytical solutions to (modified) Korteweg–de Vries–Zakharov–Kuznetsov equation and modeling ion-acoustic solitary, periodic, and breather waves in auroral magnetoplasmas

This article investigates the propagation of different types of nonlinear ion-acoustic waves, including periodic waves, solitons, and breathers in non-Maxwellian magnetized plasma. The plasma model consists of inertial cold ions, inertialess cold electrons that obey a Boltzmann distribution, and inertialess non-Maxwellian hot electrons that follow the generalized (r, q) distribution. The reductive perturbation technique is utilized to obtain the Korteweg–de Vries–Zakharov–Kuznetsov equation (KdV-ZK) from the fluid equations that govern plasma dynamics. Furthermore, the modified KdV-ZK equation is derived due to the limited capability of the KdV-ZK model to represent the dynamics of the nonlinear structures at specific critical values of the relevant physical variables in the investigated system. The periodic solutions to the two models (KdV-ZK and mKdV-ZK models) are derived using Jacobi elliptic functions. This approach directly links periodic waves (cnoidal waves) and soliton solutions. Hirota's bilinear method generates breathers for both models. Finally, we examine the quantitative understanding of the effects of several physical parameters replicated by the Swedish satellite Viking incorporated in the model. The findings reported in this study enhance our comprehension of the properties of the electron distribution function's high- and low-energy segments and the development of periodic, soliton, multi-soliton, and breather phenomena in space and astrophysical plasmas.