  We consider a Schr{\"o}dinger equation with a nonlinearity which is a general
perturbation of a power'' nonlinearity. We construct a profile decomposition
adapted to this nonlinearity.We also prove global existence and scattering in a
general defocusing setting, assuming thatthe critical Sobolev norm is bounded
in the energy-supercritical case. This generalizes severalprevious works on
double-power nonlinearities.
