Symplectic and multi-symplectic methods for coupled nonlinear Schrödinger equations with periodic solutions
Date
2007-05-18
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Computer Physics Communications
Abstract
We consider for the integration of coupled nonlinear Schrödinger equations with periodic plane wave solutions a splitting method from the class
of symplectic integrators and the multi-symplectic six-point scheme which is equivalent to the Preissman scheme. The numerical experiments
show that both methods preserve very well the mass, energy and momentum in long-time evolution. The local errors in the energy are computed
according to the discretizations in time and space for both methods. Due to its local nature, the multi-symplectic six-point scheme preserves the
local invariants more accurately than the symplectic splitting method, but the global errors for conservation laws are almost the same.
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mathematics