@article{456b123e07984906a4a13f7d07734db9,
title = "Finite difference scheme for two-dimensional periodic nonlinear Schr{\"o}dinger equations",
abstract = "A nonlinear Schr{\"o}dinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schr{\"o}dinger 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 L2 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.",
keywords = "Continuum limit, Periodic nonlinear Schr{\"o}dinger equation, Uniform Strichartz estimate",
author = "Younghun Hong and Chulkwang Kwak and Shohei Nakamura and Changhun Yang",
note = "Funding Information: Y.H. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1A2C4002615). C.K. was supported by FONDECYT Postdoctorado 2017 Proyecto No. 3170067, project France-Chile ECOS-Sud C18E06 and was supported by the Ewha Womans University Research Grant of 2020. S. N. was supported by the JSPS Grant-in-Aid for JSPS Research Fellow No. 17J01766. C.Y. was supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1702-02. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",
year = "2021",
month = mar,
doi = "10.1007/s00028-020-00585-y",
language = "English",
volume = "21",
pages = "391--418",
journal = "Journal of Evolution Equations",
issn = "1424-3199",
publisher = "Birkhauser Verlag Basel",
number = "1",
}