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

Genilson de Melo (), Marc de Montigny (), James Pinfold () and Jack Tuszynski ()
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Genilson de Melo: Universidade Federal do Recôncavo da Bahia
Marc de Montigny: University of Alberta, Faculté St Jean
James Pinfold: University of Alberta, Physics Department
Jack Tuszynski: University of Alberta, Physics Department

A chapter in Physical and Mathematical Aspects of Symmetries, 2017, pp 139-144 from Springer

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-69164-0_20

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DOI: 10.1007/978-3-319-69164-0_20

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