On instability of some approximate periodic solutions for the full nonlinear Schrödinger equation

Abstract

Using the Fermi Golden Rule analysis developed in several results by the first author, 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 of the NLS shadowed in a recent work of the second author with Michael Weinstein do not persist for the full NLS.

30 pages, 1 figure

References in corpus (4)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• A revision of "On asymptotic stability in energy space of ground states of NLS in 1D"
• Asymptotic stability of small gap solitons in the nonlinear Dirac equations
• Small solutions of nonlinear Schrödinger equations near first excited states