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Last year physicists in Europe have measured the velocity of the neutrinosparticles. They found the neutrinos moving faster than the speed of light invacuum. This result means that Einstein's relativity principle and itsconsequences in modern physics need a global additional renovation. In presentpaper the part of this problem is considered in terms of basic Maxwell's methodonly. By means of introduction a diffusion like displacement current the newsuper wave equation was derived, which permits of its solution be described theelectromagnetic waves moving some faster than the conventional speed of lightin vacuum especially in a gamma ray of a very short wave length region. Theunique properties of these waves are that they undergo nonlinear dispersionlaw, uppermost limit of which is restricted. Discussion of further experimentalproblems and a number of estimations are given for the macro physic super waveequations also.

Electromagnetic waves with nonlinear dispersion law