Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data   Revisited
  The purpose of this article is to give a streamlined and self-contained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest descent. 
Helge Krueger and Gerald Teschl