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Physical and Mathematical Aspects of Symmetries pp 139–144Cite as

Galilean complex Sine-Gordon equation: symmetries, soliton solutions and gauge coupling

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Abstract

We use the Galilean covariance formalism to obtain the Galilean complex Sine-Gordon equation in 1+1 dimensions,Ψxx (1-Ψ*Ψ)+2imΨ +Ψ*Ψ2 x – Ψ (1-Ψ*Ψ)2 = 0. We determine its Lie point symmetries, discuss some groupinvariant solutions, and examine some soliton solutions.We also discuss the coupling of this field with Galilean electromagnetism. This work is motivated in part by recent applications of the relativistic complex Sine-Gordon equation to the dynamics of Q-balls.

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Authors and Affiliations

  1. Universidade Federal do Recôncavo da Bahia, Campus Universitário de Cruz das Almas, 44380-000, Cruz das Almas, Bahia, Brazil

    Genilson de Melo

  2. Faculté St Jean, University of Alberta, Edmonton, Alberta, T6C 4G9, Canada

    Genilson de Melo & Marc de Montigny

  3. Physics Department, University of Alberta, Edmonton, Alberta, T6C 4G9, Canada

    James Pinfold & Jack Tuszynski

  4. Department of Oncology, University of Alberta, Edmonton, Alberta, T6C 4G9, Canada

    Jack Tuszynski

Authors
  1. Genilson de Melo
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  2. Marc de Montigny
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  3. James Pinfold
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  4. Jack Tuszynski
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Corresponding author

Correspondence to Genilson de Melo .

Editor information

Editors and Affiliations

  1. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Sergio Duarte

  2. Laboratoire APC, Paris Diderot University, Paris, France

    Jean-Pierre Gazeau

  3. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Sofiane Faci

  4. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Tobias Micklitz

  5. Universidade Federal Rural do Rio de Janeiro, Seropédica, Rio de Janeiro, Brazil

    Ricardo Scherer

  6. Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Rio de Janeiro, Brazil

    Francesco Toppan

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© 2017 Springer International Publishing AG

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de Melo, G., de Montigny, M., Pinfold, J., Tuszynski, J. (2017). Galilean complex Sine-Gordon equation: symmetries, soliton solutions and gauge coupling. In: Duarte, S., Gazeau, JP., Faci, S., Micklitz, T., Scherer, R., Toppan, F. (eds) Physical and Mathematical Aspects of Symmetries. Springer, Cham. https://doi.org/10.1007/978-3-319-69164-0_20

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