We derive a multi-dimensional nonlinear equation for electron-acoustic waves in magnetized plasmas composed of stationary ions, magnetized cold electrons with a significant fraction of electron beams, and magnetized hot electrons which have a non-isothermal vortex-like distribution. We find three-dimensional (3D) electron-acoustic solitary waves which have a stronger nonlinearity (in comparison with that associated with the traditional harmonic generation) due to the trapping of hot electrons in the localized electron-acoustic wave potential. The relevance of our investigation to nonlinear structures (e.g., the bipolar parallel electric fields) in the Earth's magnetosphere is discussed.