Inst High Energy Phys, Beijing 100049, Peoples R China
; Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
; Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
New explicit square-conservation schemes of any order for the nonlinear Schrodinger equation are presented. The basic idea is to discrete the space variable of the nonlinear Schrodinger equation approximately so that the resulting semi-discrete equation can be cast into an ordinary differential equation (dY)/(dt) = A(t, R)Y, A(t, Y) is a skew symmetry matrix. Then the Lie group methods, which can preserve the modulus square-conservation property of the ordinary differential equation, are applied to the ordinary differential equation. Numerical results show the effective of the Lie group method preserving the modulus square-conservation of the discrete nonlinear Schrodinger equation. (c) 2005 Elsevier Inc. All rights reserved.