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G.V.Dunne and R.Jackiw,et al.considered a nonlinear planar Schodinger equation with additional coupling to non-Abelian Chern-Simons gauge fields,they find zero-energy static solutions which satisfy self-dual equation.Then they encountered various well-known nonlinear equations with special Ansatze for lie algebraic structures within SU(N).In this report we obtain a new concrete self-dual equation and find relationship between SU(2)Chern-Simons vortices solution and topological number which is deter-
GVDunne and R. Jackiw, et al. Considered a nonlinear planar Schodinger equation with additional coupling to non-Abelian Chern-Simons gauge fields, they find zero-energy static solutions which satisfy self-dual equation. Chen them encountered various well-known nonlinear equations with special Ansatze for Lie algebraic structures within SU (N) .In this report we obtain a new concrete self-dual equation and find relationship between SU (2) Chern-Simons vortices solution and topological number which is deter-