Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials

For isotropic and homogeneous nonlinear left-handed materials, for which the effective medium approximation is valid, Maxwell's equations for electric and magnetic fields lead naturally, within the slowly varying envelope approximation, to a system of coupled nonlinear Schrödinger equations. This system is equivalent to the well-known Manakov model that under certain conditions, is completely integrable, and admits bright and dark soliton solutions. It is demonstrated that left- and right-handed (normal) nonlinear media may have compound dark and bright soliton solutions, respectively. These results are also supported by numerical calculations.