Classical electrodynamics of a nonlinear Dirac field free solutions

In previous papers it has been shown that adding a positive scalar self-interaction (ψψ)2 to the Dirac field Lagrangian provides a reasonably satisfactory model to describe the barions. In this work, we analyze other solutions of the same nonlinear Dirac equation, making progress in the direction of a systematic analysis. These solutions could provide the ground states for more elaborate interacting schemes of the real particles. Unfortunately the new solutions appear to have energies consistently higher than the ones analyzed in previous papers. Also, the more complicated solutions, whose energy seems to be much higher than the simplest one, leave us little hope for a low minimum energy state.