Exact Solution of the Landau-Lifshitz Equations for a Radiating Charged   Particle in The Coulomb Potential
  We solve exactly the classical non-relativistic Landau-Lifshitz equations of motion for a charged particle moving in a Coulomb potential, including radiation damping. The general solution involves the Painleve transcendent of type II. It confirms our physical intuition that a negatively charged classical particle will spiral into the nucleus, supporting the the validity of the Landau-Lifshitz equation. 
S. G. Rajeev