Any-order propagation of the nonlinear Schroedinger equation

TL;DR

This paper introduces an exact propagation scheme for nonlinear Schrödinger equations, analogous to linear cases, enabling improved integrator design and extending to multi-component systems.

Contribution

It presents a novel exact propagation method for nonlinear Schrödinger equations, including higher-order integrators and multi-component extensions.

Findings

Provided a simple proof for a conjecture on higher-order integrators

Extended the scheme to multi-component equations

Introduced a new class of integrators

Abstract

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.