Positron-acoustic traveling waves solutions and quasi-periodic route to chaos in magnetoplasmas featuring Cairns nonthermal distribution

Abstract

Dynamics of the positron acoustic waves (PAWs) in magnetoplasmas following Cairns non-thermal distribution is studied on the frameworks of the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations. The reductive perturbation technique is used to derive the KdV and mKdV equations. Bifurcations of positron acoustic traveling waves of these equations are addressed by employing the bifurcation theory of planar dynamical systems. It is found that the KdV equation supports compressive positron acoustic solitary waves (PASWs), while the mKdV equation supports both compressive and rarefactive PASWs. Using numerical simulations, effect of the nonthermal parameter ( $$\beta $$ ), temperature ratio of hot electron to hot positron ( $$\sigma $$ ), magnetic field ( $$\omega _{c_{1}}$$ ), ratio of hot electron to cold positron concentration ( $$\mu _{e}$$ ), and ratio of hot to cold positron concentration ( $$\mu _{p}$$ ) are discussed on the PASWs solutions of the KdV and mKdV equations. The criterion of chaos for these perturbed equations under the external periodic perturbation are obtained through quasi-periodic route to chaos. It is in fact shown that transition to chaos in our system depends on the frequency $$\omega $$ and the strength of the external periodic perturbation $$f_{0}$$ . These parameters control the dynamic behavior of the PAWs. The relevance of this work may be useful to understand the qualitative changes in the dynamics of perturbed PAWs appearing in auroral acceleration region as well as the astrophysical and laboratory plasma, where static external magnetic field and nonthermal parameter are present.