On the existence of dark solitons of the cubic nonlinear Schrodinger   equation with periodic inhomogeneous nonlinearity
  We provide a simple proof of the existence of dark solitons of the defocusing cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity. Moreover, our proof allows for a broader class of inhomogeneities and gives some new properties of the solutions. We also apply our approach to the defocusing cubic-quintic nonlinear Schrodinger equation with a periodic potential. 
Christos Sourdis
math.AP