  The nonlinear dynamics of electron-acoustic localized structures in a
collisionless and unmagnetized plasma consisting of "cool" inertial electrons,
"hot" electrons having a kappa distribution, and stationary ions is studied.
The inertialess hot electron distribution thus has a long-tailed suprathermal
(non-Maxwellian) form. A dispersion relation is derived for linear
electron-acoustic waves. They show a strong dependence of the charge screening
mechanism on excess suprathermality (through \kappa). A nonlinear
pseudopotential technique is employed to investigate the occurrence of
stationary-profile solitary waves, focusing on how their characteristics depend
on the spectral index \kappa, and the hot-to-cool electron temperature and
density ratios. Only negative polarity solitary waves are found to exist, in a
parameter region which becomes narrower as deviation from the Maxwellian
(suprathermality) increases, while the soliton amplitude at fixed soliton speed
increases. However, for a constant value of the true Mach number, the amplitude
decreases for decreasing \kappa.
