  A novel soliton-like solution in quantum electrodynamics is obtained via a
self-consistent field method. By writing the Hamiltonian of quantum
electrodynamics in the Coulomb gauge, we separate out a classical component in
the density operator of the electron-positron field. Then, by modeling the
state vector in analogy with the theory of superconductivity, we minimize the
functional for the energy of the system. This results in the equations of the
self-consistent field, where the solutions are associated with the collective
excitation of the electron-positron field---the soliton-like solution. In
addition, the canonical transformation of the variables allowed us to separate
out the total momentum of the system and, consequently, to find the
relativistic energy dispersion relation for the moving soliton.
