Analytic Aspects of the Toda System: II. Bubbling behavior and existence   of solutions
  In this paper, we continue to consider the 2-dimensional (open) Toda system (Toda lattice) for $SU(N+1)$. We give a much more precise bubbling behavior of solutions and study its existence in some critical cases 
J\"urgen Jost, Chang-Shou Lin and Guofang Wang