  A rigorous theoretical investigation has been made on electron acoustic wave
propagating in unmagnetized collisionless plasma consisting of a cold electron
fluid, non-thermal hot electrons and stationary ions. Based on the
pseudo-potential approach, large amplitude potential structures and the
existence of solitary waves are discussed. The reductive perturbation method
has been employed to derive the Korteweg-de Vries (KdV) equation for small but
finite amplitude electrostatic waves. An algebraic method with computerized
symbolic computation, which greatly exceeds the applicability of the existing
tanh, extended tanh methods in obtaining a series of exact solutions of the KdV
equation. Numerical studies have been made using plasma parameters close to
those values corresponding to the dayside auroral zone reveals different
solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with
singularity at a finite points which called blowup solutions in addition to the
propagation of an explosive pulses. The result of the present investigation may
be applicable to some plasma environments, such as terrestrial magnetosphere.
