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A theoretical investigation has been made of electron acoustic wavepropagating in unmagnetized collisionless plasma consisting of a cold electronfluid and isothermal ions with two different temperatures obeying Boltzmanntype distributions. Based on the pseudo-potential approach, large amplitudepotential structures and the existence of Solitary waves are discussed. Thereductive perturbation method has been employed to derive the Korteweg-de Vries(KdV) equation for small but finite amplitude electrostatic waves. An algebraicmethod with computerized symbolic computation, which greatly exceeds theapplicability of the existing tanh, extended tanh methods in obtaining a seriesof exact solutions of the KdV equation, is used here. Numerical studies havebeen made using plasma parameters close to those values corresponding toEarth's plasma sheet boundary layer region reveals different solutions i.e.,bell-shaped solitary pulses and singularity solutions at a finite point whichcalled "blowup" solutions, Jacobi elliptic doubly periodic wave, a Weierstrasselliptic doubly periodic type solutions, in addition to the propagation of anexplosive pulses. The result of the present investigation may be applicable tosome plasma environments, such as earth's magnetotail region and terrestrialmagnetosphere.

Solitary, explosive, rational and elliptic doubly periodic solutions for nonlinear electron-acoustic waves in the earth's magnetotail region