Exact Solution of the Landau-Lifshitz Equation in a Plane Wave

The Landau–Lifshitz (The Classical Theory of Fields. Elsevier, Oxford 1975) form of the Lorentz–Abraham–Dirac equation in the presence of a plane wave of arbitrary shape and polarization is solved exactly and in closed form. The explicit solution is presented in the particular, paradigmatic cases of a constant crossed field and of a monochromatic wave with circular and with linear polarization.