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.

A new conservative difference scheme is proposed for nonlinear Schrödinger equation, and its convergence and stability are proved. By means of numerical computing, the discretization for nonlinear term of nonlinear Schrödinger equation is discussed, and it is followed that the new difference scheme is better than the scheme of paper[7] which is a special case of the new scheme in precision, when suitable parameter is adopted.

A finite difference of energy conservation is proposed for nonlinear Klein Gordon (NKG) equation.Its convergence and stability have been proved.Results of numerical computation are also analysed.