Oblique modulation and envelope excitations of nonlinear ion sound waves with cubic nonlinearity and generalized (<i>r</i>, <i>q</i>) distribution

Abstract

The modulational instability (MI) of ion sound waves in unmagnetized collisionless electron-ion plasma is investigated by using the generalized (r, q) distribution function for electrons that mimics most of the distributions observed in space plasmas. Using the standard reductive perturbation method, a nonlinear Schrödinger equation is derived which results in the evolution of obliquely modulated ion sound envelope excitations. The effects of varying the values of double spectral indices r and q and obliqueness are explored in detail with regard to the MI. It is found that the presence of (r, q) distributed electrons drastically modifies the domain of the MI in the k−θ plane. A variety of localized ion acoustic envelope excitations like dark/gray and bright solitons are also shown to exist. The significance of the present work with special reference to space plasmas is also pointed out.