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Time splitting and error estimates for nonlinear Schrodinger equations with a potential (2408.14816v2)
Published 27 Aug 2024 in math.AP, cs.NA, math-ph, math.MP, and math.NA
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.
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