  We present a general analysis for finding and characterizing nonlinear
exceptional point (EP) lasers above threshold, using steady-state ab-initio
Maxwell-Bloch equations. For a system of coupled slabs, we show that a
nonlinear EP is obtained for a given ratio between the external pumps in each
resonator, and that it is associated with a kink in the output power and lasing
frequency, confirming coupled-mode theory predictions. Through numerical linear
stability analysis, we confirm that the EP laser can be stable for a large
enough inversion relaxation rate. We further show that the EP laser can be
characterized by scattering a weak signal off the lasing cavity, so that the
scattering frequency spectrum exhibits a quartic divergence. Our approach can
be applied to arbitrary scatterers with multi-level gain media.
