Dust-Ion-Acoustic Jacobi Cnoidal, Dnoidal and Snoidal Wave Phenomena in a Magnetized Dusty Plasma with (r, q) Distributed Electrons

Nonlinear dust-ion-acoustic waves (DIAWs) in a magnetized dusty plasma consisting of inertial ions, stationary dust particles, and (r, q) distributed electrons are studied. The technique of reductive perturbation is used to formulate the Kadomtsev-Petviashili (KP) and modified KP (mKP) equations for DIAWs. By adopting the extended Jacobi elliptic function expansion (EJEFE) method some new analytical dust-ion-acoustic wave solutions of the mKP equation are determined in terms of the Jacobi elliptic functions for the first time in the literature. The parametric effects of spectral indices (r and q), the proportion of the number density of ions to electrons ( δ _1 ), the ratio of ion gyroradius to Debye length ( γ ), direction cosine (l), and strength of magnetic field ( B_0 ) are analyzed for each wave solution. The obtained result suggests that when nonlinear structures propagate from the magnetosheath to Saturn’s magnetosphere, the waves amplify. The theoretical findings may be applicable to discern some nonlinear wave features in cosmic dusty plasmas.