Abstract: Based on  a new 2×2 discrete matrix spectral problem, we  studied conservation law and Darboux transformation of generalized Ablowitz-Ladik (AL) equation. Firstly, we gave infinite  conservation law of the generalized AL equation and obtained its explicit representation by using Riccati  method. Secondly, Darboux transformation (DT) of the generalized AL equation was constructed by means of the Lax pair and gauge  transformation. Finally,  by choosing the appropriate seed solution, we gave the explicit exact solutions of the generalized AL equation,  obtained 2-kink soliton, and analyzed the dynamic properties of the solution.

Key words: generalized Ablowitz-Ladik , equation, Lax pair, conservation law, Darboux transformation, exact solution