A symmetric low-regularity integrator for the nonlinear Schrödinger equation

2023/01/30 by Yvonne Alama Bronsard, Bronsard, Yvonne Alama · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2301.13109

openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schrödinger (NLS) equation beyond classical Fourier-based techniques. We show fractional convergence of the scheme in L²-norm, from first up to second order, both on the torus \mathbbT^d and on a smooth bounded domain Ω⊂ ℝ^d, d≤ 3, equipped with homogeneous Dirichlet boundary condition. The new scheme allows for a symmetric approximation to the NLS equation in a more general setting than classical splitting, exponential integrators, and low-regularity schemes (i.e. under lower regularity assumptions, on more general domains, and with fractional rates). We motivate and illustrate our findings through numerical experiments, where we witness better structure preserving properties and an improved error-constant in low-regularity regimes.

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• Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation

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