Geodesic
On ``characteristic'' argument functions in acoustics and electrodynamics
Matematičeskoe modelirovanie, Tome 12 (2000) no. 9, pp. 65-86.

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Continuous (differentiable) functions of “characteristic” argument are considered. Conditions of differentiability of these functions are written as system of first order differential equations for conjugate “hyperbolic” functions. Mentioned condition can be reduced to wave equation by d'Alembert for each conjugate function. Mechanical examples of conjugate hyperbolic functions are the solutions of linear equations of acoustics and electrodynamics of free space. Swirl transformations on the characteristic argument plate allow to get the linear formulas of initial independent variables transformations, which don't change d'Alembert equation and systems of acoustics and electrodynamics linear equations. At the same time with traditional Lorentz transformations for the case of subsonic (or sublight) speeds the similar transformations are obtained for the case of supersonic (or superlight) speeds. Possibility of the development of “acoustic theory of relativity” and the expansion of special theory of relativity on superlight field are demonstrated. Simulation of dark matter as gaseous medium – bearing of electromagnetic waves is also presented and such system of linear equations is written. 
@article{MM_2000_12_9_a5,
     author = {M. Ya. Ivanov},
     title = {On ``characteristic'' argument functions in acoustics and electrodynamics},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {65--86},
     publisher = {mathdoc},
     volume = {12},
     number = {9},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2000_12_9_a5/}
}
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M. Ya. Ivanov. On ``characteristic'' argument functions in acoustics and electrodynamics. Matematičeskoe modelirovanie, Tome 12 (2000) no. 9, pp. 65-86. http://geodesic.mathdoc.fr/item/MM_2000_12_9_a5/