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Volume 36, Issue 4
High Order Compact Multisymplectic Scheme for Coupled Nonlinear Schrödinger-KdV Equations

Lan Wang & Yushun Wang

DOI: 10.4208/jcm.1702-m2016-0789

J. Comp. Math., 36 (2018), pp. 591-604.

Published online: 2018-06

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  • Abstract

In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrödinger-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.

  • Keywords

Schrödinger-KdV equations, High order compact method, Conservation law, Multisymplectic scheme.

  • AMS Subject Headings

65M06, 65M12, 65Z05, 70H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wl0908@yeah.net (Lan Wang)

wangyushun@njnu.edu.cn (Yushun Wang)

  • BibTex
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  • TXT
@Article{JCM-36-591, author = {Wang , Lan and Wang , Yushun}, title = {High Order Compact Multisymplectic Scheme for Coupled Nonlinear Schrödinger-KdV Equations}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {4}, pages = {591--604}, abstract = {

In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrödinger-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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1702-m2016-0789}, url = {http://global-sci.org/intro/article_detail/jcm/12307.html} }
TY - JOUR T1 - High Order Compact Multisymplectic Scheme for Coupled Nonlinear Schrödinger-KdV Equations AU - Wang , Lan AU - Wang , Yushun JO - Journal of Computational Mathematics VL - 4 SP - 591 EP - 604 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1702-m2016-0789 UR - https://global-sci.org/intro/article_detail/jcm/12307.html KW - Schrödinger-KdV equations, High order compact method, Conservation law, Multisymplectic scheme. AB -

In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrödinger-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.

Wang , Lan and Wang , Yushun. (2018). High Order Compact Multisymplectic Scheme for Coupled Nonlinear Schrödinger-KdV Equations. Journal of Computational Mathematics. 36 (4). 591-604. doi:10.4208/jcm.1702-m2016-0789
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