  We analyze the existence, stability, and propagation of dissipative discrete
localized modes in one- and two-dimensional nonlinear lattices composed of
weakly coupled split-ring resonators (SRRs) excited by an external
electromagnetic field. We employ the near-field interaction approach for
describing quasi-static electric and magnetic interaction between the
resonators, and demonstrate the crucial importance of the electric coupling,
which can completely reverse the sign of the overall interaction between the
resonators. We derive the effective nonlinear model and analyze the properties
of nonlinear localized modes excited in one- and two-dimensional lattices. In
particular, we study nonlinear magnetic domain walls (the so-called switching
waves) separating two different states of nonlinear magnetization, and reveal
the bistable dependence of the domain wall velocity on the external field.
Then, we study two-dimensional localized modes in nonlinear lattices of SRRs
and demonstrate that larger domains may experience modulational instability and
splitting.
