Contour dynamics, waves, and solitons in the quantum Hall effect

We present a theoretical study of the excitations on the edge of a two-dimensional electron system in a perpendicular magnetic field in terms of a contour dynamics formalism. In particular, we focus on edge excitations in the quantum Hall effect. Beyond the usual linear approximation, a nonlinear analysis of the shape deformations of an incompressible droplet yields soliton solutions which correspond to shapes that propagate without distortion. A perturbative analysis is used and the results are compared to analogous systems, like vortex patches in ideal hydrodynamics. Under a local induction approximation, we find that the contour dynamics is described by a nonlinear partial differential equation for the curvature: the modified Korteweg‐de Vries equation. @S0163-1829~99!13339-3#