Any-Order Propagation of the Nonlinear Schroedinger Equation
We derive an exact propagation scheme for nonlinear Schr\o}dinger equations. This scheme is entirely analogous to the propagation of linear Schr\o}dinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)