  Localized nonlinear modes at valley-Hall interfaces in staggered photonic
graphene can be described in the long-wavelength limit by a nonlinear
Dirac-like model including spatial dispersion terms. It leads to a modified
nonlinear Schr\"odinger equation for the wave field amplitude that remarkably
incorporates a nonlinear velocity term. We show that this nonlinear velocity
correction results in a counter-intuitive stabilization effect for relatively
high-amplitude plane-wave-like edge states, which we confirm by calculation of
complex-valued small-amplitude perturbation spectra and direct numerical
simulation of propagation dynamics in staggered honeycomb waveguide lattices
with on-site Kerr nonlinearity. Our findings are relevant to a variety of
nonlinear photonic systems described by Dirac-like Hamiltonians.
