Semiclassical Nonlinear Schrodinger equations with potential and   focusing initial data
  We study the asymptotic behaviour of solutions to semi-classical nonlinear Schrodinger equations with a potential, for concentrating and oscillating initial data, when the nonlinearity is repulsive and the potential is a polynomial of degree at most two. We describe the separate roles of the nonlinearity and of the potential, with tools which seem to be specific to the class of potentials that we consider. We also discuss the case of more general subquadratic potentials. 
Remi Carles, Luc Miller