参考文献/References:
[1] LI Juan,XU Tao,MENG Xianghua,et al.Lax pair, Bäcklund transformation and N-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation[J].Journal of Mathematical Analysis and Applications,2007,336(2):1443-1455.DOI:10.1016/j.jmaa.2007.03.064.
[2] TIAN Bo,WEI Guangmei,ZHANG Chunyi,et al.Transformations for a generalized variable-coefficient Korteweg-de Vries model from blood vessels, Bose-Einstein condensates, rods and positons with symbolic computation[J].Physics Letters A,2006,356(1):8-16.DOI:10.1016/j.physleta.2006.03.080.
[3] LIU Ying,GAO Yitian,SUN Zhiyuan,et al.Multi-soliton solutions of the forced variable-coefficient extended Korteweg-de Vries equation arisen in fluid dynamics of internal solitary waves[J].Nonlinear Dynamics,2011,66(4):575-587.DOI:10.1007/s11071-010-9936-7.
[4] ZHANG Xiaohua,ZHANG Ping.A reduced high-order compact finite difference scheme based on proper orthogonal decomposition technique for KdV equation[J].Applied Mathematics and Computation,2018,339:535-545.DOI:10.1016/j.amc.2018.07.017.
[5] KONG Desong,XU Yufeng,ZHENG Zhoushun.A hybrid numerical method for the KdV equation by finite difference and sinc collocation method[J].Applied Mathematics and Computation,2019,355:61-72.DOI:10.1016/j.amc.2019.02.031.
[6] FU Guosheng,SHU Chiwang.An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-de Vries equation[J].Journal of Computational and Applied Mathematics,2019,349:41-51.DOI:10.1016/j.cam.2018.09.021.
[7] CHELLAPPAN V,GOPALAKRISHNAN S,MANI V.Spectral solutions to the Korteweg-de-Vries and nonlinear Schrödinger equations[J].Chaos, Solitons and Fractals Part A,2015,81:150-161.DOI:10.1016/j.chaos.2015.09.008.
[8] BJ?RKAVÅG M,KALISCH H.Exponential convergence of a spectral projection of the KdV equation[J].Physics Letters A,2007,365(4):278-283.DOI:10.1016/j.physleta.2006.12.085.
[9] WANG Jialing,WANG Yushun.Local structure-preserving algorithms for the KdV equation[J].Journal of Computational Mathematics,2017,35(3):289-318.DOI:10.4208/jcm.1605-m2015-0343.
[10] BRUGNANO L,GURIOLI G,SUN Yajuan.Energy-conserving Hamiltonian Boundary Value Methods for the numerical solution of the Korteweg-de Vries equation[J].Journal of Computational and Applied Mathematics,2019,351:117-135.DOI:10.1016/j.cam.2018.10.014.
[11] 房少梅.一类广义KdV方程组的谱和拟谱方法[J].计算数学,2002,24(3):353-362.DOI:10.3321/j.issn:0254-7791.2002.03.011.
[12] GUO Feng.Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation[J].Chinese Physics B,2019,28(5):24-30.DOI:10.1088/1674-1056/28/5/050201.
[13] MCLACHLAN R,PERLMUTTER M.Conformal Hamiltonian systems[J].Journal of Geometry and Physics,2001,39(4):276-300.DOI:10.1016/S0393-0440(01)00020-1.
[14] MOORE B E,NORENA L,SCHOBER C M.Conformal conservation laws and geometric integration for damped Hamiltonian PDEs[J].Journal of Computational Physics,2013,232(1):214-233.DOI:10.1016/j.jcp.2012.08.010.
[15] BHATT A FLOYD D,MOORE B E.Second order conformal symplectic schemes for damped Hamiltonian systems[J].Journal of Scientific Computing,2016,66(3):1234-1259.DOI:10.1007/s10915-015-0062-z.
[16] MOORE B E.Multi-conformal-symplectic PDEs and discretizations[J].Journal of Computational and Applied Mathematics,2017,323:1-15.DOI:10.1016/j.cam.2017.04.008.
[17] CHEN Jingbo,QIN Mengzhao.Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation[J].Electronic Transactions on Numerical Analysis Etna,2001,12:193-204.
[18] QUISPEL 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.
[19] STRANG G.On the construction and comparison of difference schemes[J].SIAM Journal on Numerical Analysis,1968,5(3):506-517.DOI:10.2307/2949700.
[20] MCLACHLAN R I,QUISPEL G R W.Splitting methods[J].Acta Numerica,2002,11:341-434.DOI:10.1017/S0962492902000053.