Abstract
Theoretical investigations depending on the observation data are carried out for the nonlinear amplitude modulation of ion-acoustic waves propagating in an unmagnetized plasma composed of Maxwellian electrons and light negative ions in addition to mobile cold positive ions. The basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE) for describing the modulational instability process. The regions of the stable and unstable wavepackets have been confined precisely for various regimes. Moreover, the criteria for the existence of the breathers have been obtained. Analytical solutions of the NLSE in the forms of Akhmediev breathers, Kuznetsov-Ma (KM) solitons, and rogue waves are obtained. The characteristics of the profile of Akhmediev breathers, KM solitons, and freak waves are examined depending on the relevant physical parameters of the observed data.