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Galilean complex sine-Gordon equation: symmetries, soliton solutions and gauge coupling. (English) Zbl 1390.35321

Duarte, Sergio (ed.) et al., Physical and mathematical aspects of symmetries. Proceedings of the 31st international colloquium in group theoretical methods in physics, Rio de Janeiro, Brazil, June 19–25, 2016. Cham: Springer (ISBN 978-3-319-69163-3/hbk; 978-3-319-69164-0/ebook). 139-144 (2017).
Summary: We use the Galilean covariance formalism to obtain the Galilean complex Sine-Gordon equation in \(1+1\) dimensions, \(\Psi_{xx}(1-\Psi^*\Psi)+2im\Psi_t+ \Psi^*\Psi^2_x-\Psi(1-\Psi^*\Psi)^2=0\). We determine its Lie point symmetries, discuss some group-invariant 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.
For the entire collection see [Zbl 1388.81008].

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
81V10 Electromagnetic interaction; quantum electrodynamics
22E70 Applications of Lie groups to the sciences; explicit representations
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