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

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 mu (i1 similar to)mu (c). Here mu (i1)=n (i10)/Z (d) n (d0), Z (d) is the number of electrons residing upon the dust grain surface, and n (i0) (n (d0)) is the lower temperature ion (dust) number density at equilibrium. These DA-GSs are completely different from the K-dV solitons, because mu (c) (the critical value) corresponds to vanishing of the nonlinear coefficient of the K-dV equation, and mu (i1)similar to mu (c) 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 mu (i1) is less than or greater than the critical value, the DA-GSs exhibit compression for mu (i1)>mu (c) and rarefaction for mu (i1)