Chern-Simons solitons, Toda theories and chiral model

The two-dimensional self-dual Chern-Simons equations are equivalent to the conditions for static, zero-energy solutions of the (2+1)-dimensional gauged nonlinear Schroedinger equation with Chern-Simons matter-gauge dynamics. In this paper we classify all finite charge SU(N) solutions by first transforming the self-dual Chern-Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck-Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between the SU(N) Tota and SU(N) chiral model solutions. (orig.)