Abstract
The Ablowitz–Ladik discrete Nonlinear Schrödinger Eq. (IDNLS) has a noncanonical symplectic structure for which standard symplectic integrators are not applicable. Using generating functions we derive higher order symplectic schemes for the IDNLS. A comparison of the efficiency of the symplectic schemes with standard Runge–Kutta algorithms with respect to accuracy and integration time is provided.
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