  We report numerical studies of the linear and nonlinear edge dynamics of a
non-harmonically confined macroscopic fractional quantum Hall fluid. In the
long-wavelength and weak excitation limit, observable consequences of the
fractional transverse conductivity are recovered. The first non-universal
corrections to the chiral Luttinger liquid theory are then characterized: for a
weak excitation in the linear response regime, cubic corrections to the linear
wave dispersion and a broadening of the dynamical structure factor of the edge
excitations are identified; for stronger excitations, sizable nonlinear effects
are found in the dynamics. The numerically observed features are quantitatively
captured by a nonlinear chiral Luttinger liquid quantum Hamiltonian that
reduces to a driven Korteweg-de Vries equation in the semiclassical limit.
Experimental observability of our predictions is finally discussed.
