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Invariant analytical solutions for the motion of an elastic string with electric current in a static magnetic field
Author(s) -
Kurmyshev Evgeny,
Piñuelas Castro Luis M.,
Yakhno Alexander,
Yakhno Liliya
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7399
Subject(s) - invariant (physics) , mathematics , homogeneous space , nonlinear system , magnetic field , string (physics) , mathematical analysis , electric field , symmetry (geometry) , classical mechanics , mathematical physics , physics , quantum mechanics , geometry
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 nonlinear 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.