Abstract
The nonlinear Schrödinger (NLS) equation has made great achievement, however the coupled nonlocal discrete nonlinear Schrödinger (CNDNLS) equations have less works. In this paper, we investigate the Darboux transformation (DT) method to obtain discrete soliton solutions of CNDNLS equations. We present two different kinds of solutions through choosing different seed solutions, and analysis the relations among them. Further many novel discrete 1-soliton and 2-soliton are derived with the zero and nonzero seed solutions. Meanwhile, the elastic interaction dynamic of two discrete solitons is displayed, it is shown that the amplitudes keep unchanged after the interactions in long time.
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