Abstract
We first establish a one-fold Darboux–Bäcklund transformation for the integrable differential-difference equation which is presented in Ref. [6] by means of a proper gauge transformation matrix. Then, as a result of the N times one-fold Darboux–Bäcklund transformation, we derive N-fold Darboux–Bäcklund transformation. Finally, using the obtained Darboux–Bäcklund transformation, two exact solutions are worked out.
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