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Effects of Radiation on sine-Gordon Coherent Structures in the Continuous and Discrete Cases

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The sine-Gordon Model and its Applications

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 10))

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Abstract

We present a modulation approach coupled with radiation to study the behavior of one and two space dimensional coherent structures in the sG equation. We show how the radiation induced motion can be coupled to the collective coordinates which describe the soliton. It is also shown how the usual geometric optics can be used to calculate the effect of two dimensional spiral waves on solitons. In turn this allows to study the stabilization of coherent solutions by internal degrees of freedom or the so-called PN effect. We point out some open questions in the last section.

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Acknowledgements

L.A. Cisneros-Ake gratefully acknowledges support from COFAA-IPN and project IPN-CGPI-20130803. L.A. Cisneros-Ake and A.A. Minzoni acknowledge support from Conacyt-177246. We acknowledge Elsevier for having given permission to reproduce Figs. 2, 4 and 5 of this chapter, which were included in [8].

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Authors and Affiliations

  1. Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738, México, D.F., México

    Luis A. Cisneros-Ake

  2. FENOMEC, Department of Mathematics and Mechanics, IIMAS, Universidad Nacional Autónoma de México, Apdo. 20-726, 01000, México, D.F., México

    A. A. Minzoni

Authors
  1. Luis A. Cisneros-Ake
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  2. A. A. Minzoni
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Corresponding author

Correspondence to Luis A. Cisneros-Ake .

Editor information

Editors and Affiliations

  1. Departamento de Físíca Aplicada I, University of Sevilla, Sevilla, Spain

    Jesús Cuevas-Maraver

  2. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Panayotis G. Kevrekidis

  3. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Floyd Williams

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Cisneros-Ake, L.A., Minzoni, A.A. (2014). Effects of Radiation on sine-Gordon Coherent Structures in the Continuous and Discrete Cases. In: Cuevas-Maraver, J., Kevrekidis, P., Williams, F. (eds) The sine-Gordon Model and its Applications. Nonlinear Systems and Complexity, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-06722-3_4

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  • DOI: https://doi.org/10.1007/978-3-319-06722-3_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06721-6

  • Online ISBN: 978-3-319-06722-3

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