Abstract
Bifurcations and chaotic behaviors of dust acoustic traveling waves in magnetoplasmas with nonthermal ions featuring Cairns–Tsallis distribution is investigated on the framework of the further modified Kadomtsev–Petviashili (FMKP) equation. The FMKP equation is derived employing the reductive perturbation technique (RPT). Bifurcations of dust acoustic traveling waves of the FMKP equation is presented. Using the bifurcation theory of planar dynamical systems, two new analytical traveling wave solutions for solitary and periodic waves are derived depending on the parameters a; a1; q; l and U. Considering an external periodic perturbation, the chaotic behavior of dust acoustic traveling waves is investigated through quasiperiodic route to chaos. The parameter q significantly affects the chaotic behavior of the perturbed FMKP equation.
Introduction
The physics of dusty plasmas is an important topic of growing research which has gained more and more interest over the last few decades not only from the academic point of view, but also from the view of its new aspects [1] in space and modern astrophysics, semiconductor technology, fusion devices, plasma chemistry, crystal physics, and biophysics. In 1989, Goertz [2] discussed collective effects in dusty plasmas which affect various waves, such as density waves in planetary rings and low-frequency plasma waves. The authors described briefly the possibility of charged grains forming a Coulomb lattice. Low temperature dusty plasmas is used in manufacturing of chips and material processing [3, 4] in industry, which is one of the greatest impacts on our everyday lives.
Conclusions
In this paper, we have derived the FMKP equation for dust acoustic waves in magnetoplasmas with nonthermal ions featuring Cairns–Tsallis distribution. Applying the bifurcation theory of planar dynamical systems to the FMKP equation, we have presented the existence of solitary and periodic traveling waves through phase plane analysis. Two new analytical solutions for the solitary waves (compressive and rarefactive) and periodic waves are obtained depending on parameters a; a1; q; l and U. Considering an external periodic perturbation, the quasiperiodic and chaotic behaviors of dust acoustic waves are studied through numerical computations. The presence of the parameters q; a; and a1 affects significantly on bifurcation of traveling wave solutions of the FMKP equation, the quasiperiodic and chaotic behaviors of the perturbed FMKP equation. It should be noted that for same set of values of parameters a; a1; q; l and U, the unperturbed FMKP equation has solitary and periodic wave solutions, but the perturbed FMKP equation shows the quasiperiodic and chaotic behaviors based on the strength of the external periodic perturbation. It is also important to note that the dust acoustic waves of the perturbed FMKP equation represent the chaotic motions through quasiperiodic route to chaos.
