Novel physical nonlinear structures in Saturn’s magnetosphere: Ion-acoustic solitons, lumps, and horseshoe-like nonlinear waves

In this paper, new analytical physical solutions to the Kadomtsev–Petviashvili–Bergers’ (KPB) equation in the multicomponent plasmas of Saturn are reported. Two distinct methods are employed to obtain various solutions to the KPB equation: the generalized Kudryashov method (gKM) and the Hirota bilinear method (HBM). Using the gKM, lump wave solution, and another solution, including a shock wave solution, are derived. Using HBM with the transformation of the auxiliary function, a new bilinear form of the KPB equation is constructed. The differences in the form of nonlinear physical structures are obtained. Based on the Hirota bilinear form, solutions for the lump wave and the one-stripe soliton wave are obtained. The propagation and interactions of the nonlinear lump soliton waves, stripe waves, and solitary waves are investigated analytically. Parametric conditions for the existence of lump waves, solitary waves, and stripe waves are presented. The importance of the current research lies in studying the behavior of the most abundant positively charged ions in Saturn’s magnetosphere, which originate from the solar wind, and of some water ions, which have also been detected and originate from Saturn’s moons, especially Titan and Enceladus.