Solving the spin-2 Gross-Pitaevskii equation using exact nonlinear   dynamics and symplectic composition
  We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order composition schemes we realize two fully symplectic integration algorithms, the first such algorithms for evolving spin-2 condensates. We demonstrate the accuracy of these algorithms against other methods on application to an exact continuous wave solution that we derive. 
L. M. Symes, P. B. Blakie
physics.comp-ph cond-mat.quant-gas