Spectral splitting method for nonlinear Schrödinger equations with quadratic potential

2021/10/27 by Andrea Sacchetti, Sacchetti, Andrea
Engineering · Mathematics · #35Q55 #65M70 #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2110.14334

openalex publication_date 2021/10/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a one-dimensional nonlinear Schroedinger equation by solving the linear problem and treating the nonlinear term separately, with a rigorous estimate of the remainder term. Furthermore, we show by means of numerical experiments that such a modified approximation is more efficient than the standard one.

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