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

TL;DR

This paper introduces symplectic numerical algorithms for solving the spin-2 Gross-Pitaevskii equation, enabling accurate and efficient simulation of spin-2 condensates through exact nonlinear dynamics.

Contribution

It develops the first symplectic integration algorithms for spin-2 condensates using exact nonlinear splitting methods and composition schemes.

Findings

Algorithms demonstrate high accuracy against existing methods.

Second- and fourth-order schemes improve simulation precision.

Validated on an exact continuous wave solution.

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.