Long Term Evolution of Close Planets Including the Effects of Secular   Interactions
  This paper studies the long term evolution of planetary systems containing short-period planets, including the effects of tidal circularization, secular excitation of eccentricity by companion planets, and stellar damping. For planetary systems subject to all of these effects, analytic solutions (or approximations) are presented for the time evolution of the semi-major axes and eccentricities. Secular interactions enhance the inward migration and accretion of hot Jupiters, while general relativity tends to act in opposition by reducing the effectiveness of the secular perturbations. The analytic solutions presented herein allow us to understand these effects over a wide range of parameter space and to isolate the effects of general relativity in these planetary systems. 
Fred C. Adams and Gregory Laughlin