A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schr?dinger equations

摘要

In this paper, a linearly implicit conservative difference scheme for the coupled nonlinear Schr?dinger equations with space fractional derivative is proposed. This scheme conserves the mass and energy in the discrete level and only needs to solve a linear system at each step. The existence and uniqueness of the difference solution are proved. The stability and convergence of the scheme are discussed, and it is shown to be convergent of order O (τ~2 + h~2) in the discrete l~2 norm with the time step τ and mesh size h. When the fractional order is two, all those results are in accord with the difference scheme proposed for the classical non-fractional coupled nonlinear Schr?dinger equations. Some numerical examples are also reported.