  The nonperturbative analysis of the one-particle excitation of the
electron-positron field is made in the paper. The standard form of quantum
electrodynamics (QED) is used but the coupling constant $\alpha_0$ is supposed
to be of a large value ($\alpha_0 \gg 1$). It is shown that in this case the
quasi-particle excitation can be produced together with the non-zero scalar
component of the electromagnetic field. Self-consistent equations for spatially
localized charge distribution coupled with an electromagnetic field are
derived. Soliton-like solution with a nonzero charge for these equations are
calculated numerically. The solution proves to be unique if the coupling
constant is fixed. It leads to the condition of charge quantization if the
non-overlapping $n$-soliton states are considered. It is also proved that the
dispersion law of the soliton-like excitation is consistent with Lorentz
invariance of the QED equations.
