Structure preserving-Field directional splitting difference methods for nonlinear Schrodinger systems

A computational framework of high order conservative finite difference methods to approximate the solution of a general system of N coupled nonlinear Schrodinger equations (N-CNLS) is proposed. Exact conservation of the discrete analogues of the mass and the system's Hamiltonian is achieved by decomposing the original system into a sequence of smaller nonlinear problems, associated to each component of the complex field, and a modified Crank-Nicolson time marching scheme appropriately designed for systems. For a particular model problem, we formally prove that a method, based on the standard second order difference formula, converges with order tau+h(2); and, using the theory of composition method, schemes of order tau(2) + h(2) and tau(4) + h(2) are derived. The methodology can be easily extended to other high order finite difference formulas and composition methods. Conservation and accuracy are numerically validated. (C) 2021 Elsevier Ltd. All rights reserved.