  We consider the edge of a two-dimensional electron system that is in the
quantum-Hall-effect regime at filling factor 1-1/m with m being an odd integer,
where microscopic theory explaining the occurrence of the quantum Hall effect
in the bulk predicts the existence of two counterpropagating edge-excitation
modes. These two modes are the classical edge-magnetoplasmon mode and a
slow-moving neutral mode. Assuming the electrons to be confined by a coplanar
neutralizing background of positive charges, and taking careful account of
long-range Coulomb interactions, we determine microscopically the velocity of
the neutral mode and the edge width. Our results are intended to guide
experimental efforts aimed at verifying the existence of the neutral mode,
which would provide a powerful confirmation of the current microscopic
understanding of quantum-Hall physics at the simplest hierarchical filling
Factors 1-1/m.
