HIGH ORDER COMPACT MULTISYMPLECTIC SCHEME FOR COUPLED NONLINEAR SCHRODINGER-KDV EQUATIONS  

作　　者：Lan Wang Yushun Wang 

机构地区：[1]Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China [2]School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

出　　处：《Journal of Computational Mathematics》2018年第4期591-604,共14页计算数学（英文）

基　　金：This work is supported by the NNSFC （Nos. 11771213, 41504078, 11301234, 11271171）, the National Key Research and Development Project of China （No. 2016YFC0600310）, the Major Projects of Natural Sciences of University in Jiangsu Province of China （No. 15KJA110002） and the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Provincial Natural Science Foundation of Jiangxi （Nos. 20161ACB20006, 20142BCB23009, 20151BAB 201012）.

摘　　要：In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing some canonical momenta. To simulate the problem efficiently, the CNLS-KdV equations are approximated by a high order compact method in space which preserves N semi-discrete multisymplectic conservation laws. We then discretize the semi-discrete system by using a symplectic midpoint scheme in time. Thus, a full-discrete multisymplectic scheme is obtained for the CNLS-KdV equations. The conservation laws of the full-discrete scheme are analyzed. Some numerical experiments are presented to further verify the convergence and conservation laws of the new scheme.In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing some canonical momenta. To simulate the problem efficiently, the CNLS-KdV equations are approximated by a high order compact method in space which preserves N semi-discrete multisymplectic conservation laws. We then discretize the semi-discrete system by using a symplectic midpoint scheme in time. Thus, a full-discrete multisymplectic scheme is obtained for the CNLS-KdV equations. The conservation laws of the full-discrete scheme are analyzed. Some numerical experiments are presented to further verify the convergence and conservation laws of the new scheme.

关 键 词：Schrodinger-KdV equations High order compact method Conservation law Multisymplectic scheme 

分 类 号：O122.2[理学—数学] O157.5[理学—基础数学]