Gardner Solitons in a Dusty Plasma

A rigorous theoretical investigation has been made on nonlinear dust-ion-acoustic (DIA) waves in a dusty plasma system, consisting of Boltzmann electrons, inertial ions, and negatively charged stationary dust. The reductive perturbation method has been employed to derive Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and standard Gardner equations. The solitary wave solutions of these equations have been analyzed. It has been shown that the K-dV and Gardner solitons (GSs) exist with positive (negative) potential for μ <; 2/3 (μ >; 2/3), where μ = Z_dn_d0/n_i0, with Z_d being the number of electrons residing onto the dust grain surface and ndo (nio) being the dust (ion) number density at equilibrium. It has also been shown that the mK-dV solitons (associated with positive potential) exist only for μ <; (1 - 1/√15). It has been finally observed that the characteristics of DIA GSs are different from those of the K-dV and mK-dV solitons.