  A theoretical investigation has been made of electron acoustic wave
propagating in unmagnetized collisionless plasma consisting of a cold electron
fluid and isothermal ions with two different temperatures obeying Boltzmann
type distributions. 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, is used here. Numerical studies have
been made using plasma parameters close to those values corresponding to
Earth's plasma sheet boundary layer region reveals different solutions i.e.,
bell-shaped solitary pulses and singularity solutions at a finite point which
called "blowup" solutions, Jacobi elliptic doubly periodic wave, a Weierstrass
elliptic doubly periodic type 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 earth's magnetotail region and terrestrial
magnetosphere.
