  We present a study of the excitations of the edge of a two-dimensional
electron droplet in a magnetic field in terms of a contour dynamics formalism.
We find that, beyond the usual linear approximation, the non-linear analysis
yields soliton solutions which correspond to uniformly rotating shapes. These
modes are found from a perturbative treatment of a non-linear eigenvalue
problem, and as solutions to a modified Korteweg-de Vries equation resulting
from a local induction approximation to the nonlocal contour dynamics. We
discuss applications to the edge modes in the quantum Hall effect.
