SELF-DUAL CHERN-SIMONS SOLITONS AND 2-DIMENSIONAL NONLINEAR EQUATIONS

The nonlinear planar Schrodinger equation with additional coupling to non-Abelian Chern-Simons gauge fields possesses static, zero-energy solutions that satisfy self-dual equations. When the Schrodinger field is in the adjoint representation, the static equations comprise a two-dimensional reduction of the four-dimensional self-dual Yang-Mills system and various zero-curvature formulations. Well-known nonlinear equations of two-dimensional physics arise for the Schrodinger field, both in the adjoint and defining representations. Thus nonrelativistic matter interacting with Chern-Simons fields provides a unified dynamical framwork for these equations.