Integrability of the semi-discrete Toda equation with self-consistent sources

A new procedure to construct and solve soliton equations with self-consistent sources (SESCSs) is applied to the semi-discrete Toda equation, based on its bilinear from. Bilinear Bäcklund transformation (BT) for the semi-discrete Toda ESCS is presented. Starting from the BT, a Lax pair is derived for the semi-discrete Toda ESCS.