A special non-linear equation of mathematical physics - the equation of   the curvilinear electromagnetic wave
  A special non-linear equation of curvilinear electromagnetic wave is presented. The particularity of this equation lies in the fact that in matrix form it is mathematically equivalent to the Dirac electron equation. It is shown that the solution of this is the motion of the plane-polarized electromagnetic wave on a circular trajectory. It is also shown that such twirled wave can be considered as a massive charge particle with a spin of one half, similar to electron. The non-linear equation and its Lagrangian of these EM particles are founded. 
Alexander G. Kyriakos