HIGH ORDER COMPACT MULTISYMPLECTIC SCHEME FOR COUPLED NONLINEAR SCHR(O)DINGER-KDV EQUATIONS

• 来源期刊: 计算数学（英文版）
• 关键词: Schr(o)dinger-KdV equations High order compact method Conservation law Multisymplectic scheme
• 年，卷（期）: 2018,（4）
• 页码范围: 591-604
• 页数: 14页
• 语种: 英文
• DOI: 10.4208/jcm.1702-m2016-0789

摘要

In this paper,a novel multisymplectic scheme is proposed for the coupled nonlinearSchr(o)dinger-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.