Time splitting and error estimates for nonlinear Schrodinger equations with a potential

2024/08/27 by Carles, Rémi · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2408.14816

Abstract

We consider the nonlinear Schrödinger 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.

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• Computing nonlinear Schrödinger equations with Hermite functions beyond harmonic traps

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