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

In this paper, we develop a new kind of multisymplectic integrator for the coupled nonlinear Schrödinger (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.