Modulational instability of ion-acoustic waves has been theoretically investigated in an unmagnetized collisionless plasma with nonthermal electrons, Boltzmann positrons, and warm positive ions. To describe the nonlinear evolution of the wave amplitude a nonlinear Schr？dinger (NLS) equation has been derived by using multiple scale perturbation technique. The nonthermal parameter, positron concentration, and ion temperature are shown to play significant role in the modulational instability of ion-acoustic waves and the formation of envelope solitons. 1. Introduction Electron-positron-ion ( - - ) plasmas occur in many astrophysical environments such as active galactic nuclei [1], pulsar magnetospheres [2], polar regions of neutron stars [3], centres of our galaxy [4], the early universe [5, 6], and the solar atmosphere [7]. For this, over the last two decades there has been a great deal of interest in the study of nonlinear wave phenomena in - - plasmas [8–12]. Positrons are produced by pair production in high energy processes occurring in many astrophysical environments. Popel et al. [9] have reported decrease in soliton amplitude in the presence of positrons. Jehan et al. [13] have shown that solitons become narrower as the concentration of positron increases. The presence of non-Maxwellian electron is common in space and astrophysical plasmas including the magnetosphere [12] and auroral zones [14]. The presence of such non-Maxwellian electrons gives rise to many interesting characteristics in the nonlinear propagation of waves including the ion-acoustic solitons [15, 16]. The solitary structures with density depression in the magnetosphere observed by the Freja satellites [17, 18] have been explained by Cairns et al. [19] by assuming electron distribution to be nonthermal. Nonlinear ion-acoustic solitary waves in - - plasma have been considered by some authors [9, 20, 21] assuming ions to be cold. In practice ions have finite temperature and the ionic temperature can significantly affect the characteristics of nonlinear ion-acoustic structures [10, 22, 23]. Chawla et al. [24] have considered ion-acoustic waves in - - plasma with warm adiabatic ions and isothermal electrons. Baluku and Hellberg [25] have considered ion-acoustic solitary waves in - - plasma with cold ions and nonthermal electrons. Hence it is interesting to study the nonlinear ion-acoustic waves in - - plasma assuming simultaneous presence of nonthermal electrons, warm negative ions, and the positrons. Recently Pakzad [11] has shown that the presence of warm ions and nonthermal electrons
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