This paper presents analytical solutions that we obtained in extending the BGK electron solitary wave solutions in 1D to include the 3D electrical interaction (E ~ 1/r2) of charged particles. Our results indicate that for a single humped electric potential, the parallel cut of the perpendicular component of the electric field (E⊥) is unipolar and that of the parallel component (E∥) bipolar. The multi-dimensional features of solitary waves have been observed by the FAST satellite. The parallel width-amplitude relation is found to be an inequality and it depends on the perpendicular scale size of the solitary structure. This feature can be used in conjunction with experimental data to obtain an estimate on the typical perpendicular size of observed solitary waves.