title: Solving the spin-2 Gross-Pitaevskii equation using exact nonlinear dynamics and symplectic composition.
abstract: 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.
authors.affiliation: Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin 9016, New Zealand.
authors.forename: L M
authors.initials: LM
authors.lastname: Symes
authors.affiliation: Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin 9016, New Zealand.
authors.forename: P B
authors.initials: PB
authors.lastname: Blakie