Ultra-short solitons and kinetic effects in nonlinear metamaterials
  We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation for the pulses, making it possible to analyze and describe partial coherence in metamaterials. It is shown that a novel short pulse soliton, which is found analytically, can propagate in the medium. 
M. Marklund, P. K. Shukla, and L. Stenflo