Nonlinear magnetoinductive waves and domain walls in composite   metamaterials
  We describe novel physics of nonlinear magnetoinductive waves in left-handed composite metamaterials. We derive the coupled equations for describing the propagation of magnetoinductive waves, and show that in the nonlinear regime the magnetic response of a metamaterial may become bistable. We analyze modulational instability of different nonlinear states, and also demonstrate that nonlinear metamaterials may support the propagation of domain walls (kinks) connecting the regions with the positive and negative magnetization. 
Ilya V. Shadrivov, Alexander A. Zharov, Nina A. Zharova, and Yuri S.   Kivshar