article

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

Authors: Jeremy Marzuola and Scipio Cuccagna

Issue: Volume 61 (2012), Issue 6, 2053-2083

Abstract:

$Using the Fermi Golden Rule analysis developed in [S. Cuccagna and T. Mizumachi, \textit{On asymptotic stability in energy space of ground states for nonlinear Schr\"odinger equations}, Comm. Math. Phys. \textbf{284} (2008), no. 1, 51--77], we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schr\"odinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions for the cubic Nonlinear Schr\"odinger Equation (NLSE) with symmetric potential in [J.\:L. Marzuola and M.\:I. Weinstein, \textit{Long time dynamics near the symmetry breaking bifurcation for nonlinear Schr\"odinger/Gross-Pitaevskii equations}, Discrete Contin. Dyn. Syst. \textbf{28} (2010), no. 4, 1505--1554] do not persist in the comparable quintic NLSE.$