Staeckel systems generating coupled KdV hierarchies and their finite-gap   and rational solutions
  We show how to generate coupled KdV hierarchies from Staeckel separable systems of Benenti type. We further show that solutions of these Staeckel systems generate a large class of finite-gap and rational solutions of cKdV hierarchies. Most of these solutions are new. 
Maciej Blaszak and Krzysztof Marciniak