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arXiv · 1103.0198

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

Scipio Cuccagna·Jeremy L. Marzuola
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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.

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Scipio Cuccagna, Jeremy L. Marzuola. 2011-03-01. On instability of some approximate periodic solutions for the full nonlinear Schrödinger equation. https://arxiv.org/abs/1103.0198

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