Efficient invariant-preserving scheme for the N-coupled nonlinear Schrödinger equations

The N -coupled nonlinear Schr & ouml;dinger equations are reformulated into an expanded form by using a scalar auxiliary variable method, and then a scheme preserving exactly original mass and energy conservation laws is proposed based on discretizing the expanded form. The scheme is efficient as it consists of decoupled linear systems with constant coefficients, along with a nonlinear algebraic equation that can be solved with negligible computational cost. Some numerical experiments are carried out to demonstrate the behavior of wave solutions, the accuracy of solution and the preservation of physical invariants.