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