LOCALIZED SOLUTIONS OF ONE-DIMENSIONAL NONLINEAR DIRAC EQUATIONS WITHPOINT INTERACTION POTENTIALS

We find the exact localized solutions of a class of nonlinear Dirac eq uations perturbed by a point interaction potential, thal is, any sharp ly peaked potential approaching the delta-function limit. A detailed a nalysis of the existence conditions of these localized solutions is ca rried out. We show that our results agree with non-relativistic predic tions when both the self-coupling and the point interaction potential are weak. Lower bounds to the size of the localized solutions are pres ented.