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

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 syrnplectic 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.