Construction of solutions for an integrable differential-difference equation by Darboux–Bäcklund transformation

摘要

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.