Ion Acoustic Solitary Wave Solutions to mKdV-ZK Model in Homogeneous Magnetized Plasma

In this exploration, we reflect on the wave transmission of three-dimensional (3D) nonlinear electron–positron magnetized plasma, counting both hot as well as cold ion. Treated equation acquiesces to nonlinear-modified KdV-Zakharov–Kuznetsov (mKdV-ZK) dynamical 3D form. The model is integrated by the ${\phi }^6$ -model expansion scheme and invented few families of ion acoustic solitonic propagation results in term of Jacobi elliptic functions. Various shock waves, bullet like bright soliton, dark soliton, singular soliton, as well as periodic signal solutions, are formed from the Jacobi elliptic solution for different parametric constraints. Some of the solutions are illustrated graphically and analyzed width and height due to change of exist parameters in the solutions. Figures are provided to explain the wave natures and effects of nonlinear and fractional parameters are presented in the same two-dimensional (2D) plots.