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Invariant analytical solutions for the motion of an elastic string with electric current in a static magnetic field
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  • Evgeny Kurmyshev,
  • Luis Manuel Piñuelas Castro,
  • Alexander Yakhno,
  • Liliya Yakhno
Evgeny Kurmyshev
Universidad de Guadalajara Centro Universitario de Los Lagos
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Luis Manuel Piñuelas Castro
Universidad de Guadalajara
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Alexander Yakhno
Universidad de Guadalajara Centro Universitario de Ciencias Exactas e Ingenieria
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Liliya Yakhno
Universidad de Guadalajara Centro Universitario de Ciencias Exactas e Ingenieria
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Abstract

In this work, the Lie symmetry theory is used to study the propagation of waves in an elastic string with electric currents in a static magnetic field. Both linear and nonlin- ear cases of the governing equations of string motion are analyzed. The classification problem of finding the principal admitted Lie groups of symmetries is solved. Some invariant analytical solutions are constructed. The physics of invariant solutions is interpreted when it is possible.

Peer review status:Published

11 Aug 2020Submitted to Mathematical Methods in the Applied Sciences
12 Aug 2020Submission Checks Completed
12 Aug 2020Assigned to Editor
21 Aug 2020Reviewer(s) Assigned
10 Feb 2021Review(s) Completed, Editorial Evaluation Pending
11 Feb 2021Editorial Decision: Revise Major
01 Mar 20211st Revision Received
02 Mar 2021Submission Checks Completed
02 Mar 2021Assigned to Editor
03 Mar 2021Reviewer(s) Assigned
10 Mar 2021Review(s) Completed, Editorial Evaluation Pending
12 Mar 2021Editorial Decision: Accept
07 Apr 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.7399