Spectral splitting method for nonlinear Schr\"odinger equations with quadratic potential

DOI10.1016/J.JCP.2022.111154arXiv2110.14334MaRDI QIDQ6381421

Publication date: 27 October 2021

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.

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) General mathematical topics and methods in quantum theory (81Qxx)

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