ZHANG H, SONG S H, CHEN X D, et al. Average Vector Field Methods for the Coupled Schrödinger-KdV Equations[J]. Chinese Physics B, 2014, 23(7):242-250.
SUN J Q, GU X Y, MA Z Q. Numerical Study of the Soliton Waves of the Coupled Nonlinear Schrödinger System[J]. Physical D:Nonlinear Phenomena, 2004, 196(3/4):311-328.
冯康, 秦孟兆.哈密尔顿系统的辛几何法[M].杭州:浙江科学技术出版社, 2003.
QIN M Z, ZHU W J. Construction of High Order Symplectic Schemes by Composition[J]. Computing, 1992, 47(3-4):309-321. doi: 10.1007/BF02320199
WANG Y S, WANG B, QIN M Z. Local Structure-Preserving Algorithms for Partial Differential Equations[J]. Science in China series A:Mathematics, 2008, 51(11):2115-2136. doi: 10.1007/s11425-008-0046-7
CELLEDONI E, MCLACHLAN R I, OWEREN B, et al. On Conjugate B-Series and Their Geometric Structure[J]. Journal of Numerical Analysis Industrial and Applied Mathematics, 2010, 5(1-2):85-94.
CHEN J B, QIN M Z, TANG Y F. Symplectic and Multi-Symplectic Methods for the Nonlinear Schrödinger Equation[J]. Computers and Mathematics with Applications, 2002, 43(8-9):1095-1106. doi: 10.1016/S0898-1221(02)80015-3
CHARTIER P, FAOU E, MURUA A. An Algebraic Approach to Invariat Preserving Integators:The Case of Quadratic and Hamiltonian Invariants[J]. Numerische Mathematik, 2006, 103(4):575-590. doi: 10.1007/s00211-006-0003-8
QUISPE G R W, MCLAREN D I. A New Class of Energy-Preserving Numerical Integration Methods[J]. Journal of Physics A:Mathematical and Theoretical, 2008, 41(4):045206. doi: 10.1088/1751-8113/41/4/045206
MCLACHLAN R I, QUISPEL G R W, ROBIDOUX N. Geometric Integration Using Discrete Gradients[J]. Philosophical Trasaction of the Royal Society A:Mathematic Physical and Engineering Science, 1999, 357(1754):1021-1045. doi: 10.1098/rsta.1999.0363
CELLEDOIN E, MCLACHLAN R I, OWREN B, et al. Energy-Preserving Intergrators and the Structure of B-Series[J]. Foundations of Computational Mathematics, 2010, 10(6):673-693. doi: 10.1007/s10208-010-9073-1