  We derive an exact propagation scheme for nonlinear Schroedinger equations.
This scheme is entirely analogous to the propagation of linear Schroedinger
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.
