High Order Compact Multisymplectic Scheme for Coupled Nonlinear Schrödinger-KdV Equations (Journal of Computational Mathematics, 2018)
In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinearSchrödinger-KdV (CNLS-KdV) equations. The CNLS-KdV equations are rewritten intothe multisymplectic Hamiltonian form by introducing some canonical momenta. To simulatethe problem efficiently, the CNLS-KdV equations are approximated by a high ordercompact method in space which preserves $N$ semi-discrete multisymplectic conservationlaws. We then discretize the semi-discrete system by using a symplectic midpoint schemein 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 numericalexperiments are presented to further verify the convergence and conservation laws of thenew scheme.
Keywords: Schrödinger-KdV equations; High order compact method; Conservation law; Multisymplectic scheme.