We consider the Bogomol’nyi equations of the Abelian Chern–Simons–Higgs model with SU(N)globalU(1)local symmetry. This is a generalization of the well-known Abelian Chern–Simons–Higgs model with U(1)local symmetry. We prove existence of both topological and nontopological multivortex solutions of the system on the plane.

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