Spectral splitting method for nonlinear Schr\"odinger equations with quadratic potential
Mathematical Physics
2022-03-17 v2 Numerical Analysis
math.MP
Numerical Analysis
Abstract
In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a one-dimensional nonlinear Schroedinger equation by solving the linear problem and treating the nonlinear term separately, with a rigorous estimate of the remainder term. Furthermore, we show by means of numerical experiments that such a modified approximation is more efficient than the standard one.
Cite
@article{arxiv.2110.14334,
title = {Spectral splitting method for nonlinear Schr\"odinger equations with quadratic potential},
author = {Andrea Sacchetti},
journal= {arXiv preprint arXiv:2110.14334},
year = {2022}
}
Comments
20 pages, 3 figures