Gardner Solitons in a Dusty Plasma

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d0</sub> /n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i0</sub> , with Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> 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.