On instability for the quintic nonlinear Schrodinger equation of some approximate periodic solutions

Using the Fermi Golden Rule analysis developed in \cite{cuccagnamizumachi}, we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schr\"odinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions of the NLS in work by Marzuola and Weinstein do not persist for the quintic NLS.