The nonlinear propagation of electron acoustic waves (EAWs) in a plasma composed of a cold electron fluid, hot electrons obeying trapped/vortex-like distribution, warm electron beam, and stationary ions is considered. The streaming velocity of the beam, uo, plays the dominant role in changing the topology of the linear dispersion relation. For small but finite amplitude EAWs, a modified Korteweg de Vries (MKdV) equation is derived. It is found that the MKdV supports EAWs having a positive potential, which corresponds to a hole (hump) in the cold (hot) electron number density. The energy soliton amplitude decreases, though its width increases for any increase in the beam parameters. In the vicinity of the isothermal population, a nonlinear evolution equation with mixed nonlinearity is obtained. Its solution gives a (compressive/rarefactive) soliton or a compressive double layer (DL) depending on the system parameters. For arbitrary amplitude EAWs, the exact Sagdeev potential has been derived. The admitted Mach number regime widens due to an increase of the beam parameters. With a better approximation in the Sagdeev potential, more features of solitary waves, e.g., spiky and explosive, are also highlighted. The introduced effects modify significantly the wave velocity, the amplitude, and the width of the EAWs investigated numerically. This theoretical model is in good agreement with the broadband noise emission observed by Geotail spacecraft in the plasma sheet boundary layer of the Earth's magnetosphere.