Choreographies in the Discrete Nonlinear Schr\"odinger Equations
Dynamical Systems
2018-11-14 v1
Abstract
We study periodic solutions of the discrete nonlinear Schr\"{o}dinger equation (DNLSE) that bifurcate from a symmetric polygonal relative equilibrium containing sites. With specialized numerical continuation techniques and a varying physically relevant parameter we can locate interesting orbits, including infinitely many choreographies. Many of the orbits that correspond to choreographies are stable, as indicated by Floquet multipliers that are extracted as part of the numerical continuation scheme, and as verified \textit{a posteriori} by simple numerical integration. We discuss the physical relevance and the implications of our results.
Cite
@article{arxiv.1801.03187,
title = {Choreographies in the Discrete Nonlinear Schr\"odinger Equations},
author = {Renato Calleja and Eusebius Doedel and Carlos García-Azpeitia and Carlos L. Pando},
journal= {arXiv preprint arXiv:1801.03187},
year = {2018}
}