Spectral method and Bayesian parameter estimation for the space fractional coupled nonlinear Schrödinger equations
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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 Schrödinger 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.
KeywordsSpace fractional coupled nonlinear Schrödinger equations Legendre spectral method Mass and energy conservation Convergence analysis Bayesian parameter estimation
We would like to express our gratitude to the Editor for taking time to handle the manuscript and to anonymous referees whose constructive comments are very helpful for improving the quality of our paper. This work was supported financially by National Natural Science Foundation of China (Grants Nos. 11472161, 11102102), Natural Science Foundation of Shandong Province (Grant No. ZR2014AQ015) and Independent Innovation Foundation of Shandong University (Grant No. 2013ZRYQ002).
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Conflict of interest
The authors declare that they have no conflict of interests regarding the publication of this paper.
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