Analysis of some new conservative schemes for nonlinear Schrödinger equation with wave operator

Some new conservative finite difference schemes are presented for an initial-boundary value problem of Schrödinger equation with wave operator. They have the advantages that there are some discrete energies which are conserved respectively. The existence of the solution of the finite difference schemes are proved by Leray–Schauder fixed point theorem. And the uniqueness, stability and convergence of difference solutions with order O(h2 + τ2) are proved in the energy norm. Results of numerical experiment demonstrate the efficiency of the new scheme.