  For the Schr\"odinger equation with a cubic-quintic, focusing-focusing
nonlinearity in one space dimension, this article proves the local asymptotic
completeness of the family of small standing solitary waves under even
perturbations in the energy space. For this model, perturbative of the
integrable cubic Schr\"odinger equation for small solutions, the linearized
equation around a small solitary wave has an internal mode, whose contribution
to the dynamics is handled by the Fermi golden rule.
