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Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation. (English) Zbl 1050.65127
Summary: The Hamiltonian and the multi-symplectic formulations of the nonlinear Schrödinger equation are considered. For the multi-symplectic formulation, a new six-point difference scheme which is equivalent to the multi-symplectic Preissman integrator is derived. Numerical experiments are also reported.

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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