Compressive and rarefactive dust-acoustic Gardner solitons beyond the K-dV limit with two-temperature ions dusty plasma

Abstract

The Gardner equation is derived and numerically solved. This equation shows the existence of compressive and rarefactive dust-acoustic (DA) solitons with two-temperature ions beyond the K-dV (Korteweg–de Vries) limit. These may be referred to as DA Gardner solitons (DA-GSs). Here we deal with a dusty plasma, composed of negatively charged cold mobile dust fluids, inertialess Boltzmann electrons and ions with two distinctive temperatures. The basic features of the compressive and rarefactive DA solitons are identified. These solitons are found to exist beyond the K-dV limit, i.e. they exist for μi1∼μc. Here μi1=ni10/Zdnd0, Zd is the number of electrons residing upon the dust grain surface, and ni0 (nd0) is the lower temperature ion (dust) number density at equilibrium. These DA-GSs are completely different from the K-dV solitons, because μc (the critical value) corresponds to vanishing of the nonlinear coefficient of the K-dV equation, and μi1∼μc corresponds to K-dV solitons, with extremely large amplitude, for which the validity of the reductive perturbation method breaks down. It has been found that, depending on whether the parameter μi1 is less than or greater than the critical value, the DA-GSs exhibit compression for μi1>μc and rarefaction for μi1<μc. The basic features of double layers with arbitrary amplitude are also briefly discussed, employing the pseudo-potential approach. The present investigation might be relevant to the electrostatic solitary structures observed in various cosmic dust-laden plasmas, such as supernova shells, Saturn’s F-ring, the ionopause of Halley’s comet, etc.