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arXiv · 1904.09640

Finite difference scheme for two-dimensional periodic nonlinear Schr\"odinger equations

Younghun Hong·Chulkwang Kwak·Shohei Nakamura·Changhun Yang
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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 $L^2$ 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.

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Younghun Hong, Chulkwang Kwak, Shohei Nakamura, Changhun Yang. 2019-04-21. Finite difference scheme for two-dimensional periodic nonlinear Schr\"odinger equations. https://arxiv.org/abs/1904.09640

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