Geophysical Journal | 2008 volume 30 1

Symmetry properties and their use in solving Maxwell equations in heterogeneous media

© Tsifra I.M., Messina A., Chizhitskiy T.

It has been found that Maxwell equations in the medium are invariant in relation to infinitely parametric Lie group, in which connection basis elements of corresponding Lie algebra contain four arbitrary functions. It has been shown that the system of equations of Maxwell together with material equation of Minkovsky in moving medium is conformly-invariant the same way as equations for electromagnetic field in vacuum. Analytical solution of Maxwell equations in the medium has been plotted with the help of method of group reduction. It has been shown how symmetry is used for plotting the solutions of the whole class of heterogeneous media from the solution for homogeneous medium. The results obtained can be successfully used for testing numerical methods of solving the problems of geo-electrics in heterogeneous media.

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