Geodesic
Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
Electronic transactions on numerical analysis, Tome 12 (2001), pp. 193-204
Bridges and Reich suggested the idea of multi-symplectic spectral discretization on Fourier space [4]. Based on their theory, we investigate the multi-symplectic Fourier pseudospectral discretization of the nonlinear Schr $\ddot $odinger equation (NLS) on real space. We show that the multi-symplectic semi-discretization of the nonlinear Schr $\ddot $odinger equation with periodic boundary conditions has N (the number of the nodes) semi-discrete multisymplectic conservation laws. The symplectic discretization in time of the semi-discretization leads to N fulldiscrete multi-symplectic conservation laws. We also prove a result relating to the spectral differentiation matrix.
Classification : 65M99
Keywords: multi-symplectic, Fourier pseudospectral method, nonlinear schr $\ddot $odinger equation 
@article{ETNA_2001__12__a3,
     author = {Chen,  Jing-Bo and Qin,  Meng-Zhao},
     title = {Multi-symplectic {Fourier} pseudospectral method for the nonlinear {Schr\"odinger} equation},
     journal = {Electronic transactions on numerical analysis},
     pages = {193--204},
     year = {2001},
     volume = {12},
     zbl = {0980.65108},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2001__12__a3/}
}
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AU  - Qin,  Meng-Zhao
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EP  - 204
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UR  - http://geodesic.mathdoc.fr/item/ETNA_2001__12__a3/
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%A Qin,  Meng-Zhao
%T Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
%J Electronic transactions on numerical analysis
%D 2001
%P 193-204
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%U http://geodesic.mathdoc.fr/item/ETNA_2001__12__a3/
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%F ETNA_2001__12__a3
Chen,  Jing-Bo; Qin,  Meng-Zhao. Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation. Electronic transactions on numerical analysis, Tome 12 (2001), pp. 193-204. http://geodesic.mathdoc.fr/item/ETNA_2001__12__a3/