Spectral method and Bayesian parameter estimation for the space fractional coupled nonlinear Schrodinger equations

摘要

In a lot of dynamic processes, the fractional differential operators not only appear as discrete fractional, but they also have a continuous nature in some sense. In the article, we consider the space fractional coupled nonlinear Schrodinger equations. A Legendre spectral scheme is proposed for obtaining the numerical solution of the considered equations. The convergence analysis of the numerical method is discussed, and it is shown to be convergent of spectral accuracy in space and second-order accuracy in time. The conservation laws of the fully discrete system are analyzed rigorously. Moreover, the Bayesian method is given to estimate many parameters of this system. Some numerical results are presented to verify the effectiveness of the proposed approaches.