Dynamic behavior of the (3+1)-dimensional generalized Johnson model in a dusty plasma

Abstract

In this paper, we study the (3+1)-dimensional generalized Johnson model, which can be used to describe the dust-ion-acoustic waves in a cosmic unmagnetized dusty plasma, and its perturbed model, which can be found in an unmagnetized dusty plasma for the electron temperature below the Curie temperature. (I) For the original model: Bilinear form and soliton solutions are obtained. Amplitude of the one soliton reaches the maximum when the equilibrium electron (ne0) and ion (ni0) densities take certain values which correspond withne0/ni0= 2. Overtaking and head-on interactions between the two solitons are given. (II) For the perturbed model: Phase projections are given numerically. Via the spectral analysis, two kinds of chaotic motions, i.e., the weak and developed chaos, are investigated. Largest Lyapunov exponents and power spectra are investigated to corroborate that those motions are indeed chaotic. Dynamic behavior of such a perturbed model varying with the external perturbation is different when the nonlinear term changes. With the damped term considered, two kinds of periodic motions are studied, and spectra of those periodic motions are also given. Through the comparison between the chaotic motions and periodic ones, possible chaotic or periodic motions in the perturbed model can be predicted.