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We investigate the long-time asymptotics for the focusing integrable discretenonlinear Schr\"odinger equation. Under generic assumptions on the initialvalue, the solution is asymptotically a sum of 1-solitons. We find differentphase shift formulas in different regions. Along rays away from solitons, thebehavior of the solution is decaying oscillation. This is one way of statingthe soliton resolution conjecture. The proof is based on the nonlinear steepestdescent method.

Long-Time Asymptotics for the integrable discrete nonlinear Schr\"odinger equation: The Focusing Case