High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations

Authors:
Yuanping Ma;Linghua Kong;Jialin Hong;Ying Cao
Affiliations:
School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, PR China;School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, PR China;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, P.O. Box 2719, Beijing, 100190, PR China;School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, PR China
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, we develop a new kind of multisymplectic integrator for the coupled nonlinear Schrodinger (CNLS) equations. The CNLS equations are cast into multisymplectic formulation. Then it is split into a linear multisymplectic formulation and a nonlinear Hamiltonian system. The space of the linear subproblem is approximated by a high-order compact (HOC) method which is new in multisymplectic context. The nonlinear subproblem is integrated exactly. For splitting and approximation, we utilize an HOC-SMS integrator. Its stability and conservation laws are investigated in theory. Numerical results are presented to demonstrate the accuracy, conservation laws, and to simulate various solitons as well, for the HOC-SMS integrator. They are consistent with our theoretical analysis.