Problematic solutions to the Landau-Lifshitz equation
  A critical look at the Landau-Lifshitz equation, which has been recently advocated as an "exact" relativistic classical equation for the motion of a point charge with radiation reaction, demonstrates that it generally does not conserve energy-momentum. Its failure is dramatic in the one-dimensional case of a stepped electric field, where it predicts discontinuous velocity and thus infinite radiation. The Lorentz-Dirac equation, on the other hand, in spite of its preacceleration over distances comparable to the classical electron radius, does not display such problems. 
W. E. Baylis and J. Huschilt