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

Abstract

ABSTRACT. Using the Fermi Golden Rule analysis developed in[CM], we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schrödinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions for the cubic Nonlinear Schrödinger Equation (NLSE) with symmetric potential in [MW] do not persist in the comparable quintic NLSE.