Evolution of ion-acoustic solitary waves in an inhomogeneous discharge plasma

Abstract

The physical processes in the generation of a solitary wave through a special nonlinear wave equation, called the Korteweg–deVries (K–dV) equation [D. J. Korteweg and G. deVries, Philos. Mag. 39, 422 (1895)], have been studied in an ideal inhomogeneous plasma incorporating the electric field and low current discharges. It is concluded that the usual procedure, because of the plasma inhomogeneity and ionization, is not suitable to exhibit soliton propagation unless an assumption for a mathematical simplification is made. Despite that, the soliton solution does not satisfactorily correspond to experiments. A new approach has been applied for finding the exact soliton propagation with a view to relating the observation to that expected exactly in an experiment. The results let one evaluate the formation of a tailing structure, which follows the main soliton with a growing nature as a function of the plasma configuration. Finally, the theoretical observations seem to significantly stimulate the observations in laboratory and space plasmas.