Turbulence of lump, stripe, and soliton waves in Saturn's magnetosphere plasmas

The Zakharov–Kuznetsov equation, along with its modified forms [the modified Zakharov–Kuznetsov and further modified Zakharov–Kuznetsov equations], is important modeling equations for interpreting different magnetoacoustic waves in plasma. In this study, we established stable broad-ranging soliton solutions, including well-known lump- and stripe-shaped soliton solutions, obtained using the Hirota bilinear (HB) method. The figures in this text show the effect of physical parameters in the plasma system—dispersion and turbulent dispersion coefficients—on wave height. Wave heights remain determinable for different values of the physical parameters and the free parameters associated with them. A three-dimensional (3D) plot of the ascertained solutions clarified the stability points of the equations we studied based on the bifurcation theory. The results for each modeling equation make a significant contribution to the analysis of dust-ion-acoustic waves in plasma in Saturn's magnetosphere. We assert that the HB method is reliable, appropriate, easy to use, and powerful for extracting closed-form soliton solutions.