The attributes of the dust-acoustic solitary and periodic structures in the Saturn's inner magnetosphere

Nonlinear characteristics of dust-acoustic (DA) structures including the localized and periodic waves in a plasma having Maxwellian ions and superthermal two-temperature electrons are investigated. The wave equations, including both Kadomtsev-Petviashvili (KP) and modified KP (mKP) equations, are derived using the reductive perturbation technique (RPT). The quantitative and qualitative characteristics of both compressive and rarefactive structures are studied. The Jacobi elliptic function expansion method (JEFEM) is employed for the purpose of quantitative analysis, while the qualitative behavior is studied by the dint of the dynamical system approach. The solutions to the mKP equation hold under a critical condition where the quadratic nonlinearity ceases to exist. It is noticed that the KP equation admits only rarefactive solitary waves (SWs), whereas the mKP equation admits both compressive and rarefactive SWs. It is found that the profile (amplitude and width) of both DA solitary and periodic structures are different at different radii of Saturn's inner magnetosphere. The effect of the kappa spectral index is studied, and it is found that when the population of energetic cold electrons is decreased, the solitary structure gets energized. Our study is applied to Saturn's inner magnetosphere where kappa distributed two-temperature electrons and dust grains with negative charge are observed by various satellite missions.