Interaction of dust ion acoustic solitons with cubic nonlinearity in a magnetized dusty plasma with (r, q) distributed electrons

Dust ion acoustic waves (DIAWs) are analysed in multi-component plasmas via reductive perturbation technique comprising inertial ions, (r, q) distributed electrons, and stationary dust by using fluid theory of plasmas. The modified Kadomtsev-Petviashvili (MKP) equation is obtained for the critical condition at which the quadratic nonlinearity vanishes. Hirota's bilinear formalism is employed, for the first time, to study the two-soliton solutions of MKP equation in the context of plasma physics. The effects of flatness at low energy (represented by r) and superthermality at high energy (represented by q) of electrons in phase space are investigated for the linear and nonlinear propagation of DIAWs. It is found that the amplitude of the nonlinear DIAW is highest for the flat-topped distribution, whereas it is lowest for kappa distribution. Using the plasma parameters of Saturn's B-ring. The estimates are given of the spatial scales over which the MKP solitons form for flat-topped, kappa, and Maxwellian distributions, respectively. It is also discussed in detail how the presence of dust and non-Maxwellian electron distributions affect the interaction of MKP solitons in Saturn's B-ring. In addition, the interaction of a compressive and rarefactive soliton is studied giving results not achievable for KdV and KP equations. (© 2022 Wiley‐VCH GmbH.)