Variable separation approach for a differential-difference system:   special Toda equation
  A multi-linear variable separation approach is developed to solve a differential-difference Toda equation. The semi-discrete form of the continuous universal formula is found for a suitable potential of the differential-difference Toda system. Abundant semi-discrete localized coherent structures of the potential can be found by appropriately selecting the arbitrary functions of the semi-discrete form of the universal formula. 
Xian-min Qian, Sen-yue Lou and Xing-biao Hu