| [1] Guo X, Xu M. Some physical applications of fractional Schrödinger equation[J]. Journal of mathematical physics, 2006, 47(8):082104.[2] Longhi S. Fractional Schrödinger equation in optics[J]. Optics letters, 2015, 40(6):1117-1120.[3] Kirkpatrick K, Lenzmann E, Staffilani G. On the continuum limit for discrete NLS with long-range lattice interactions[J]. Communications in mathematical physics, 2013, 317(3):563-591.[4] Duo S, Zhang Y. Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation[J]. Computers & Mathematics with Applications, 2016, 71(11):2257-2271.[5] Wang P, Huang C. An energy conservative difference scheme for the nonlinear fractional Schrödinger equations[J]. Journal of Computational Physics, 2015, 293:238-251.[6] Wang P, Huang C. Structure-preserving numerical methods for the fractional Schrödinger equation[J]. Applied Numerical Mathematics, 2018, 129:137-158.[7] Bouard A D, Debussche A. The Stochastic Nonlinear Schrödinger Equation in H1[J]. Anal. Appl., 2003, 21(1):97-126.[8] Liu J. A mass-preserving splitting scheme for the stochastic Schrödinger equation with multiplicative noise[J]. IMA Journal of Numerical Analysis, 2013, 33(4):1469-1479.[9] Jiang S, Wang L, Hong J. Stochastic multi-symplectic integrator for stochastic nonlinear Schrödinger equation[J]. Communications in Computational Physics, 2013, 14(2):393-411.[10] Zhou W, Zhang L, Hong J, Song S. Projection methods for stochastic differential equations with conserved quantities[J]. BIT Numerical Mathematics, 2016, 56(4):1497-1518.[11] Zhou W, Zhang J, Hong J, Song S. Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise[J]. Journal of Computational and Applied Mathematics, 2017, 325:134-148.[12] Liang J, Qian X, Shen T, Song S. Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise[J]. Journal of Mathematical Analysis and Applications, 2018, 466(2):1525-1544.[13] Yang Q, Liu F, Turner I. Numerical methods for fractional partial differential equations with Riesz space fractional derivatives[J]. Applied Mathematical Modelling, 2010, 34(1):200-218.[14] Atangana A, Secer A. A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions[J]. Abstr. Appl. Anal., 2013, 2013(1):215-222.[15] Evans L C. An Introduction to Stochastic Differential Equations[M]. American Mathematical Soc., 2012.[16] Lord G J, Powell C E, Shardlow T. An Introduction to Computational Stochastic PDEs[M]. Cambridge University Press, 2014.[17] Wei L, Zhang X, Kumar S, Yildirim A. A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrödinger system[J]. Computers & Mathematics with Applications, 2012, 64(8):2603-2615.[18] Zhang D, Zhang Y, Zhang Z, Ahmed N, Zhang Y, Li F, Beli? M R, Xiao M. Unveiling the link between fractional Schrödinger equation and light propagation in honeycomb lattice[J]. Annalen der Physik, 2017, 529(9):1700149.[19] Hong J, Ji L, Zhang L, Cai J. An energy-conserving method for stochastic Maxwell equations with multiplicative noise[J]. Journal of Computational Physics, 2017, 351:216-229.[20] Chen C, Hong J. Symplectic Runge-Kutta Semidiscretization for Stochastic Schrödinger Equation[J]. SIAM Journal on Numerical Analysis, 2016, 54(4):2569-2593. |
