Electromagnetic localization and existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band where the magnetic permeability μ(ω) is positive and the dielectric permittivity ǫ(ω) is negat...

The paper studies existence of ground states for the nonlinear Schrödinger equation 0.1 $$\begin{aligned} -(\nabla + {\mathbf {i}}A(x))^2u+V(x)u=|u|^{p-1}u ,\quad 2<p<2^*, \end{aligned}$$ with a general external magnetic field. In particular, no lattice periodicity or symmetry field, presence electric field is required.