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Choreographies in the discrete nonlinear Schrödinger equations

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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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Authors and Affiliations

  1. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México, Mexico

    Renato Calleja

  2. Department of Computer Science, Concordia University, Montreal, Canada

    Eusebius Doedel

  3. Facultad de Ciencias, Universidad Nacional Autónoma de México, México, Mexico

    Carlos García-Azpeitia

  4. Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

    Carlos L. Pando L.

Authors
  1. Renato Calleja
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  2. Eusebius Doedel
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  3. Carlos García-Azpeitia
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  4. Carlos L. Pando L.
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Correspondence to Eusebius Doedel.

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Calleja, R., Doedel, E., García-Azpeitia, C. et al. Choreographies in the discrete nonlinear Schrödinger equations. Eur. Phys. J. Spec. Top. 227, 615–624 (2018). https://doi.org/10.1140/epjst/e2018-00135-x

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  • DOI: https://doi.org/10.1140/epjst/e2018-00135-x

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