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

DOI10.1512/IUMJ.2012.61.4911zbMATH Open1292.35275arXiv1103.0198OpenAlexW2068452822MaRDI QIDQ2874070

Publication date: 28 January 2014

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1103.0198

zbMATH Keywords

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Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcations in context of PDEs (35B32)

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