Abstract The Gardner equation, showing the existence of compressive and rarefactive dust-acoustic (DA) solitons in a nonextensive dusty plasma (containing negatively charged dust, Maxwellian ions and two-temperature electrons following a q-nonextensive distribution) beyond the K-dV (Korteweg-de Vries) limit, is derived and numerically solved. The basic features of the DA Gardner solitons (GSs) associated with positive and negative potentials are found to exist beyond the K-dV limit, and the K-dV and modified K-dV (mK-dV) solitons have been compared with the DAGSs by considering the effects of two-temperature electron’s nonextensivity. Depending on the nonextensive parameter q, the DAGSs have been found to exhibit negative (positive) potential solitons for q < q c (q > q c ) (where q c is the critical value of q). The results obtained from this analysis can be utilized and should be very effective for understanding the localized nonlinear structures, the DAGSs, in different astrophysical and cosmological scenarios (viz. stellar polytropes, quark-gluon plasma, protoneutron stars, etc.).
Abstract Nonlinear dust-acoustic solitary waves which are described with a Kortweg-de vries (KdV) equation by using the reductive perturbation method, are investigated in a planar unmagnetized dusty plasma consisting of electrons, positrons, ions and negatively-charged dust particles of different sizes and masses. The effects of the power-law distribution of dust and other plasma parameters on the dust-acoustic solitary waves are studied. Numerical results show that the dust size distribution has a significant influence on the propagation properties of dust-acoustic solitons. The amplitudes of solitary waves in the case of a power-law distribution is observed to be smaller, but the soliton velocity and width are observed to be larger, than those of mono-sized dust grains with an average dust size. Our results indicate that only compressed solitary waves exist in dusty plasma with different dust species. The relevance of the present investigation to interstellar clouds is discussed.