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Starting from the Maxwell equations, we used the reductive perturbationmethod to derive a system of two coupled nonlinear Schr\"{o}dinger (NLS)equations for the two Beltrami components of the electromagnetic fieldpropagating along a fixed direction in an isotropic nonlinear chiralmetamaterial. With single-resonance Lorentz models for the permittivity andpermeability and a Condon model for the chirality parameter, in certainspectral regimes, one of the two Beltrami components exhibits a negative realrefractive index when nonlinearity is ignored and the chirality parameter issufficiently large.We found that, inside such a spectral regime, there mayexist a subregime wherein the system of the NLS equations can be approximatedby the Manakov system. Bright-bright, dark-dark, and dark-bright vectorsolitons can be formed in that spectral subregime.

Vector solitons in nonlinear isotropic chiral metamaterials