  The nonlinear propagation of electrostatic solitary waves is studied in a
collisionless electron-positron pair plasma consisting of adiabatic cool
electrons, mobile cool positrons (or electron holes), hot suprathermal
electrons described by a $\kappa$ distribution, and stationary ions. The linear
dispersion relation derived for electrostatic waves demonstrates a weak
dependence of the phase speed on physical conditions of positrons in
appropriate ranges of parameters. The Sagdeev's pseudopotential approach is
used to obtain the existence of electrostatic solitary wave structures,
focusing on how their characteristics depend on the physical conditions of
positrons and suprathermal electrons. Both negative and positive polarity
electrostatic solitary waves are found to exist in different ranges of Mach
numbers. As the positrons constitute a small fraction of the total number
density, they slightly affect the existence domains. However, the positrons can
significantly change the wave potential at a fixed soliton speed. The results
indicate that the positive potential can greatly be grown by increasing the
electron suprathermality (lower $\kappa$) at a fixed true Mach number. It is
found that a fraction of positrons maintain the generation of positive polarity
electrostatic solitary waves in the presence of suprathermal electrons in pair
plasmas.
