• cond-mat.mes-hall
• cond-mat.str-el

We study the non-linear effects beyond the standard chiral Luttinger liquid theory for the edge excitations of a fractional quantum Hall liquid with filling factor ν=1/m. In the limit of small momenta, the most excited state is a fermionic particle-hole excitation with charge √ν. For large momenta, the most excited state is the quantum counterpart of the classical Korteweg-de-Vries soliton and it can be described via a symmetry-breaking ansatz of soliton coherent states. We develop the semiclassical theory for coherent states, we use it to compute the first quantum corrections to key observables and to investigate the surprising time evolution of the soliton coherent state.