Keywords: 
• topological number /
• vortex /
• JackiwPi model

Abstract: By using the gauge potential decomposition, we have discussed the selfdual equation and its solution in JackiwPi model. We obtained a new concrete selfdual equation and find relationship between ChernSimons vortex solution and topological number which is determined by Hopf indices and Brouwer degrees of mapping. To show the meaning of topological number we presented several figures with different topological numbers. In order to investigate the topological properties of many vortices, 5 parameters (two positions, one scale, one phase per vortex and one charge of each vortex) have been used to describe each vortex in many vortices solution in JackiwPi model. For many vortices, three figures with different topological numbers have been drown to show the effect of the charge on the many vortices solution. We also studied the quantization of flux of those vortices related to the topological numbers in this case.