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R.Jackiw and S.Y.Pi considered a gauged,nonliner Sch(?)dinger equation in two spatial dimensions, which describes nonrelativistic matter interacting with Chern-Simons gauge fields.Then they find explicit static,self-dual solutions which satisfies the Liouville equation.In this report we obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees,in order to investigate the topological properties of many vortices,we use 5 parameters to describe each vortex in many vortices solutions in Jackiw-Pi mod- el.The Abelian Jackiw-Pi model in nonlinear Schr(?)dinger systems is
R. Jackiw and SYPi considered a gauged, nonliner Sch (?) Dinger equation in two spatial dimensions, which describes nonrelativistic matter interacting with Chern-Simons gauge fields. If they find explicit static, self-dual solutions which satisfies the Liouville equation. In this report we obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees, in order to investigate the topological properties of many vortices, we use 5 parameters to describe each vortex in many vortices solutions in Jackiw-Pi mod- el. The Abelian Jackiw-Pi model in nonlinear Schr (?) dinger systems is