Abstract
In this paper, we propose two local conservative methods for solving two-dimensional nonlinearSchrodinger equation. Without consideration of the boundary conditions, they can preserve corresponding local energy and momentum conservation laws exactly at arbitrary spatial-temporal regions. Meanwhile, the charge, global energy and global momentum conservation laws can be conserved under suitable boundary conditions.Numerical analysis, including conservative properties and error estimation analysis, are investigated.Furthermore, a similar multi-symplectic Preissman scheme is constructed as comparison.Numerical experiments show the advantages of the proposed methods during long-time numerical simulations and validate the analysis.
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