Quantum Hall Edges with Hard Confinement: Exact Solution beyond   Luttinger Liquid
  We consider a Laughlin droplet in a confining potential which is very steep but also weak compared to the ultra-short ranged inter-particle interactions. We find that the eigenstates have a Jack polynomial structure, and have an energy spectrum which is extremely different from the well-known Luttinger liquid edge. 
Richard Fern and Steven H. Simon
cond-mat.str-el