Abstract
We discuss a new equation, the Galilean version of the complex Sine-Gordon equation in 1+1 dimensions, Ψxx(1−Ψ⁎Ψ)+2imΨt+Ψ⁎Ψx2−Ψ(1−Ψ⁎Ψ)2=0, derived from its relativistic counterpart via Galilean covariance. We determine its Lie point symmetries, discuss some group-invariant solutions, and examine some soliton solutions. The reduction under Galilean symmetry leads to an equation similar to the stationary Gross–Pitaevskii equation. This work is motivated in part by recent applications of the relativistic complex Sine-Gordon equation to the dynamics of Q-balls.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
