Variable separation approach for a differential-difference system: special Toda equation

Abstract

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. PACS numbers:02.30.Ik, 05.45.Yv 1