English

On instability of some approximate periodic solutions for the full nonlinear Schr\"odinger equation

Analysis of PDEs 2011-03-02 v1

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 Schr\"odinger 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.

Keywords

Cite

@article{arxiv.1103.0198,
  title  = {On instability of some approximate periodic solutions for the full nonlinear Schr\"odinger equation},
  author = {Scipio Cuccagna and Jeremy L. Marzuola},
  journal= {arXiv preprint arXiv:1103.0198},
  year   = {2011}
}

Comments

30 pages, 1 figure