Solitons in finite droplets of noncommutative Maxwell-Chern-Simons theory

We find soliton solutions of the noncommutative Maxwell-Chern-Simons theory confined to a finite quantum Hall droplet. The solitons are exactly as hypothesized in \cite{Manu}. We also find new variations on these solitons. We compute their flux and their energies. The model we consider is directly related to the model proposed by Polychronakos\cite{Poly} and studied by Hellerman and Van Raamsdonk\cite{HvR} where it was shown that it is equivalent to the quantum Hall effect.