On the modulational stability of Gross-Pittaevskii type equations in 1+1   dimensions
  The modulational stability of the nonlinear Schr{\"o}dinger (NLS) equation is examined in the cases with linear and quadratic external potential. This study is motivated by recent experimental studies in the context of matter waves in Bose-Einstein condensates. The linear case can be examined by means of the Tappert transformation and can be mapped to the NLS in the appropriate (constant acceleration) frame. The quadratic case can be examined by using a lens-type transformation that converts it into a regular NLS with an additional linear growth term. 
Z. Rapti, P.G. Kevrekidis and V.V. Konotop