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Self-dual vortex solutions are studied in detail in the generalized abelianHiggs model with independent Chern-Simons interaction. For special choices ofcouplings, it reduces to a Maxwell-Higgs model with two scalar fields, aChern-Simons-Higgs model with two scalar fields, or other new models. Weinvestigate the properties of the static solutions and perform detailednumerical analyses. For the Chern-Simons-Higgs model with two scalar fields inan asymmetric phase, we prove the existence of multisoliton solutions which canbe viewed as hybrids of Chern-Simons vortices and $CP^1$ lumps. We also discusssolutions in a symmetric phase with the help of the corresponding exactsolutions in its nonrelativistic limit. The model interpolating all threemodels---Maxwell-Higgs, Chern-Simons-Higgs, and $CP^1$ models--- is discussedbriefly. Finally we study the possibility of vortex solutions with half-integervorticity in the special case of the model. Numerical results are negative.Comment: 32 pages, LATEX, SNUTP 92-7

Self-dual vortices in the generalized Abelian Higgs model with independent Chern-Simons interaction