Modulational instability of spatially broadband nonlinear optical pulses   in four-state atomic systems
  The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A comparison between coherent and random phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultra-short optical pulses. In practical terms, this could be achieved by using random phase plate techniques. 
M. Marklund, P. K. Shukla, R. Bingham, J. T. Mendonca