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We propose a family of reliable symplectic integrators adapted to theDiscrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H.Yoshida, Construction of higher order symplectic integrators, Physics LettersA, 150, 5,6,7, (1990), pp. 262.) we can construct high order numerical schemes,that result to be explicit methods and thus very fast. The performances of theintegrators are discussed, studied as functions of the integration time stepand compared with some non symplectic methods.

High order explicit symplectic integrators for the Discrete Non Linear Schr\"odinger equation