Rogue waves in electronegative space plasmas: The link between the family of the KdV equations and the nonlinear Schrödinger equation

Abstract

We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg–de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrödinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.