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

In: Physical and Mathematical Aspects of Symmetries

Author

Listed:
  • Genilson de Melo

    (Universidade Federal do Recôncavo da Bahia
    University of Alberta, Faculté St Jean)

  • Marc de Montigny

    (University of Alberta, Faculté St Jean)

  • James Pinfold

    (University of Alberta, Physics Department)

  • Jack Tuszynski

    (University of Alberta, Physics Department
    University of Alberta, Department of Oncology)

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.

Suggested Citation

  • Genilson de Melo & Marc de Montigny & James Pinfold & Jack Tuszynski, 2017. "Galilean complex Sine-Gordon equation: symmetries, soliton solutions and gauge coupling," Springer Books, in: Sergio Duarte & Jean-Pierre Gazeau & Sofiane Faci & Tobias Micklitz & Ricardo Scherer & Francesco To (ed.), Physical and Mathematical Aspects of Symmetries, pages 139-144, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-69164-0_20
    DOI: 10.1007/978-3-319-69164-0_20
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