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While symplectic integration methods based on operator splitting are wellestablished in many branches of science, high order methods for Hamiltoniansystems that split in more than two parts have not been studied in greatdetail. Here, we present several high order symplectic integrators forHamiltonian systems that can be split in exactly three integrable parts. Weapply these techniques, as a practical case, for the integration of thedisordered, discrete nonlinear Schroedinger equation (DDNLS) and compare theirefficiencies. Three part split algorithms provide effective means tonumerically study the asymptotic behavior of wave packet spreading in the DDNLS- a hotly debated subject in current scientific literature.

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High order three part split symplectic integrators: Efficient techniques  for the long time simulation of the disordered discrete nonlinear  Schroedinger equation