Exact solution to the Landau-Lifshitz equation in a constant   electromagnetic field
  We are interested in the motion of a classical charge acted upon an external constant electromagnetic field where the back reaction of the particle's own field is taken into account. The Landau-Lifshitz approximation to the Lorentz-Abraham-Dirac equation is solved exactly and in closed form. It is shown that the ultrarelativistic limit of the Landau-Lifshitz equation for a radiating charge is the equation for eigenvalues and eigenvectors of the external electromagnetic field tensor. 
Yurij Yaremko
hep-th