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We develop numerical methods for solving the spin-2 Gross-Pitaevskiiequation. The basis of our work is a two-way splitting of this evolutionequation that leads to two exactly solvable subsystems. Utilizing second-orderand fourth-order composition schemes we realize two fully symplecticintegration algorithms, the first such algorithms for evolving spin-2condensates. We demonstrate the accuracy of these algorithms against othermethods on application to an exact continuous wave solution that we derive.

Solving the spin-2 Gross-Pitaevskii equation using exact nonlinear dynamics and symplectic composition