Characteristic behavior and modulation instability of Peregrine solitons of the ion acoustic waves: a perspective of Titan’s ionosphere

Abstract

The propagational properties of solitons along with peregrine solitonic modulational instability of ion acoustic (IA) waves are investigated taking into account the plasma properties of the Titan’s ionosphere. The Titan’s ionosphere typically consists of positive (, , and ) and negative (, , and ) ionic species along with electrons. In this study, it is assumed that the positive ions and electrons follow the Lorentzian-like kappa distribution. The fluid model equations are considered for negative ions. The Korteweg-de Vries (KdV) equation is derived using the reductive perturbation method to study the propagational properties and the characteristic behavior of solitons. In addition, the multiple-scale perturbation method is also used to derive the non-linear Schrödinger (NLS) equation for the analyses of modulational instability along with the production of rogue waves considering Peregrine solitonic solution. The dark solitons appear for the smaller wave numbers, whereas the bright solitons appear for the larger wave numbers. On the other hand, instability due to modulation is excited when the wave number is greater than its critical value, whereas it becomes stable when the wave number is smaller. The Peregrine soliton carries a single pick that decays to the plane wave asymptotic background either in space or time domain.