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Finite difference scheme for two-dimensional periodic nonlinear Schrodinger equations

Title
Finite difference scheme for two-dimensional periodic nonlinear Schrodinger equations
Authors
Hong, YounghunKwak, ChulkwangNakamura, ShoheiYang, Changhun
Ewha Authors
곽철광
SCOPUS Author ID
곽철광scopus
Issue Date
2021
Journal Title
JOURNAL OF EVOLUTION EQUATIONS
ISSN
1424-3199JCR Link

1424-3202JCR Link
Citation
JOURNAL OF EVOLUTION EQUATIONS vol. 21, no. 1, pp. 391 - 418
Keywords
Periodic nonlinear Schrodinger equationUniform Strichartz estimateContinuum limit
Publisher
SPRINGER BASEL AG
Indexed
SCIE; SCOPUS WOS
Document Type
Article
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.
DOI
10.1007/s00028-020-00585-y
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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