Eur. Phys. J. Special Topics 227, 615–624 (2018)
https://doi.org/10.1140/epjst/e2018-00135-x

Regular Article

Choreographies in the discrete nonlinear Schrödinger equations

¹ Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México, Mexico
² Department of Computer Science, Concordia University, Montreal, Canada
³ Facultad de Ciencias, Universidad Nacional Autónoma de México, México, Mexico
⁴ Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

^a e-mail: doedel@cs.concordia.ca

Received: 14 December 2017
Received in final form: 24 March 2018
Published online: 4 October 2018

Abstract

We study periodic solutions of the discrete nonlinear Schrödinger equation (DNLSE) that bifurcate from a symmetric polygonal relative equilibrium containing n 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 a posteriori by simple numerical integration. We discuss the physical relevance and the implications of our results.