Computing nonlinear Schr\"odinger equations with Hermite functions beyond harmonic traps
Numerical Analysis
2026-04-14 v2 Numerical Analysis
Abstract
Hermite basis functions are a powerful tool for the spatial discretisation of Schr\"odinger equations with harmonic potential. In this work, we show that their stability properties extend to the simulation of Schr\"odinger equations without harmonic potential, thus making them a natural basis for the computation of nonlinear dispersive equations on unbounded domains. Building on this spatial discretisation, we introduce a novel unconditionally stable numerical method for the derivative nonlinear Schr\"odinger equation. Our theoretical results are supported with extensive numerical examples.
Cite
@article{arxiv.2512.20840,
title = {Computing nonlinear Schr\"odinger equations with Hermite functions beyond harmonic traps},
author = {Valeria Banica and Georg Maierhofer and Katharina Schratz},
journal= {arXiv preprint arXiv:2512.20840},
year = {2026}
}