The propagation dynamics of nonlinear electron acoustic waves (EAW) are explored analytically and numerically in collisionless unmagnetized plasmas. The dynamics of the nonlinear wave is shown to be governed by a Boussinesq equation. In the supersonic range, the wave becomes unstable in the short wave limit. In the nonlinear stage, this unstable mode reaches a maximum values and after that it damps. Different limiting cases of the general solutions are discussed. Analytical and computational results predict that the nonlinear EAW possesses breather structures apart from the usual solitary wave solutions. The results are discussed in the context of astrophysical plasmas. © 2021 Elsevier B.V.