Study on Abundant Dust-Ion-Acoustic Solitary Wave Solutions of a (3+1)-Dimensional Extended Zakharov-Kuznetsov Dynamical Model in a Magnetized Plasma and Its Linear Stability

This article examines how shocks and three-dimensional nonlinear dust-ion-acoustic waves propagate across uniform magnetized electron-positron-ion plasmas. The two-variable (G '/G,1/G)-expansion and generalized exp(-phi(xi))-expansion techniques are presented to construct the ion-acoustic wave results of a (3+1)-dimensional extended Zakharov-Kuznetsov (eZK) model. As a result, the novel soliton and other wave solutions in a variety of forms, including kink- and anti-kink-type breather waves, dark and bright solitons, kink solitons, and multi-peak solitons, etc., are attained. With the help of software, the solitary wave results (that signify the electrostatic potential field), electric and magnetic fields, and quantum statistical pressures are also constructed. These solutions have numerous applications in various areas of physics and other areas of applied sciences. Graphical representations of some of the obtained results, and the electric and magnetic fields as well as the electrostatic field potential are also presented. These results demonstrate the effectiveness of the presented techniques, which will also be useful in solving many other nonlinear models that arise in mathematical physics and several other applied sciences fields.