Time splitting and error estimates for nonlinear Schrodinger equations with a potential
Analysis of PDEs
2025-07-22 v3 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
We consider the nonlinear Schr{\"o}dinger equation with a potential, also known as Gross-Pitaevskii equation. By introducing a suitable spectral localization, we prove low regularity error estimates for the time discretization corresponding to an adapted Lie-Trotter splitting scheme. The proof is based on tools from spectral theory and pseudodifferential calculus in order to obtain various estimates on the spectral localization, including discrete Strichartz estimates which support the nonlinear analysis.
Cite
@article{arxiv.2408.14816,
title = {Time splitting and error estimates for nonlinear Schrodinger equations with a potential},
author = {Rémi Carles},
journal= {arXiv preprint arXiv:2408.14816},
year = {2025}
}
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