Finite difference scheme for two-dimensional periodic nonlinear Schr\"odinger equations
Analysis of PDEs
2019-04-23 v1
Abstract
A nonlinear Schr\"odinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schr\"odinger 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 to those of the NLS as the grid size approaches zero. As a result, the effectiveness of the finite difference method (FDM) is justified for the two-dimensional periodic NLS.
Cite
@article{arxiv.1904.09640,
title = {Finite difference scheme for two-dimensional periodic nonlinear Schr\"odinger equations},
author = {Younghun Hong and Chulkwang Kwak and Shohei Nakamura and Changhun Yang},
journal= {arXiv preprint arXiv:1904.09640},
year = {2019}
}
Comments
25 pages