Any-order propagation of the nonlinear Schrödinger equation

We derive an exact propagation scheme for nonlinear Schrödinger equations. This scheme is entirely analogous to the propagation of linear Schrödinger 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 multicomponent equations, and to a new class of integrators.