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The European Physical Journal Special Topics

, Volume 227, Issue 5–6, pp 615–624 | Cite as

Choreographies in the discrete nonlinear Schrödinger equations

  • Renato Calleja
  • Eusebius Doedel
  • Carlos García-Azpeitia
  • Carlos L. Pando L.
Regular Article
Part of the following topical collections:
  1. Nonlinear Phenomena in Physics: New Techniques and Applications

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.

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Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Renato Calleja
    • 1
  • Eusebius Doedel
    • 2
  • Carlos García-Azpeitia
    • 3
  • Carlos L. Pando L.
    • 4
  1. 1.Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de MéxicoMéxicoMexico
  2. 2.Department of Computer ScienceConcordia UniversityMontrealCanada
  3. 3.Facultad de Ciencias, Universidad Nacional Autónoma de MéxicoMéxicoMexico
  4. 4.Instituto de Física, Benemérita Universidad Autónoma de PueblaPueblaMexico

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