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| TITLE | Finite difference scheme for two-dimensional periodic nonlinear Schrodinger equations |
|---|---|
| KIAS AUTHORS | Yang, Changhun |
| JOURNAL | JOURNAL OF EVOLUTION EQUATIONS, 2021 |
| ARCHIVE | |
| ABSTRACT | A nonlinear Schrodinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrodinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations. We show that in two spatial dimensions, solutions to the DNLS converge strongly in L-2 to those of the NLS as the grid size h > 0 approaches zero. As a result, the effectiveness of the finite difference method (FDM) is justified for the two-dimensional periodic NLS. |
