Bifurcation analysis for dust ion acoustic waves in magnetized four-component plasmas with superthermal electrons

Abstract

In collisionless, dissipative, and magnetized dusty plasma, the propagation of nonlinear dust-ion-acoustic (DIA) solitary and shock waves has been studied, whose constituents are cold positive ions, negative ions obeying the Boltzmann distribution, superthermally distributed electrons and positively charged stationary dust particles. The Korteweg-de Vries–Burgers (KdVB) equation is derived using the reductive perturbation method. This equation is solved using the tangent hyperbolic method, yielding a shock wave solution. Also, other interesting physical solutions and the corresponding electric field are determined. By applying the bifurcation theory to the planar dynamical system of the derived KdVB equation under two conditions and , the presence of solitary wave solutions and periodic traveling wave solutions has been established. According to both numerical and analytical investigations, The basic properties of dust ion acoustic waves are significantly modified by the influence of superthermal electrons, viscosity coefficients, and the existence of an external magnetic field. The current results could help in a full understanding and studying of plasma waves in both space and astrophysical environments (such as the magnetospheres of Saturn and pulsars) and also in the laboratory.