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 - <p style="text-align: justify;">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.</p>