The Akhmediev Breather is unstable
Analysis of PDEs
2019-08-20 v2
Abstract
In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in [17], in the sense that a suitable modification of the Stokes wave is the global attractor of the local Akhmediev dynamics for sufficiently large time, and therefore the latter cannot be stable in any suitable finite energy periodic Sobolev space.
Keywords
Cite
@article{arxiv.1810.12543,
title = {The Akhmediev Breather is unstable},
author = {Miguel A. Alejo and Luca Fanelli and Claudio Muñoz},
journal= {arXiv preprint arXiv:1810.12543},
year = {2019}
}
Comments
Submitted to the Proceedings of the \emph{Third Workshop on Nonlinear Dispersive Equations}, held in Campinas, Brazil, during November 8-10 2017. Revised version. Accepted in SPJM