Abstract: A linear difference scheme which is not coupled for a coupled nonlinear Schrodinger system is proposed. It is shown that the scheme reserves conservation of the original system. It is demonstrated with a discrete energy method that the scheme is unconditionally stable and convergent by second-order L₂ in norm on basis of some priori estimates. Collision of two solitary waves is simulated.

Key words: coupled SchrÖdinger equations, linear scheme, uncoupled scheme, conservation, convergence