Multi-symplectic Fourier Pseudospectral Method for the Nonlinear Schrödinger Equation
نویسندگان
چکیده
Abstract. 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 Schrödinger equation (NLS) on real space. We show that the multi-symplectic semi-discretization of the nonlinear Schrödinger 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. Numerical experiments are included to demonstrate the remarkable local conservation properties of multi-symplectic spectral discretizations.
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