Local structure-preserving algorithms for the nonlinear Schrödinger equation with power law nonlinearity

This paper introduces three local structure-preserving algorithms for the one-dimensional nonlinear Schrödinger equation with power law nonlinearity, comprising two local energy-conserving algorithms and one local momentum-conserving algorithm. Additionally, we extend these local conservation algori...

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 484; p. 128986
Main Authors:	Luo, Fangwen, Tang, Qiong, Huang, Yiting, Ding, Yanhui, Tang, Sijia
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.01.2025
Subjects:	Global conservation Local conservation Nonlinear Schrödinger equation Power law nonlinearity Structure-preserving algorithms Local conservation Structure-preserving algorithms Nonlinear Schrödinger equation Global conservation Power law nonlinearity
ISSN:	0096-3003
Online Access:	Get full text
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Summary:	This paper introduces three local structure-preserving algorithms for the one-dimensional nonlinear Schrödinger equation with power law nonlinearity, comprising two local energy-conserving algorithms and one local momentum-conserving algorithm. Additionally, we extend these local conservation algorithms to achieve global conservation under periodic boundary conditions. Theoretical analyses confirm the conservation properties of these algorithms. In numerical experiments, we validate the advantages of these algorithms in maintaining long-term energy or momentum conservation by comparing them with a multi-symplectic Preissman algorithm. •Developed three local structure-preserving algorithms.•The power law nonlinearity is discretized by Crank-Nicolson method.•The conservation of the local algorithm is proved theoretically.
ISSN:	0096-3003
DOI:	10.1016/j.amc.2024.128986