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A multisymplectic integrator for the periodic nonlinear Schrödinger equation. (English) Zbl 1103.65130
Summary: A multisymplectic integrator for the periodic nonlinear Schrödinger equation is presented in this paper. Its accuracy is proved. By introducing a norm, we investigate its nonlinear stability. We also discuss the relationship between this multisymplectic integrator and two variational integrators which are derived by using the discrete multisymplectic field theory and the finite element method.

65P10Numerical methods for Hamiltonian systems including symplectic integrators
35Q55NLS-like (nonlinear Schrödinger) equations
37M15Symplectic integrators (dynamical systems)
Full Text: DOI
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