Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle

The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic sche...

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Autores principales: Wei, Yi, Zhang, Xing-Qiu, Shao, Zhu-Yan, Gao, Jian-Qiang, Yang, Xiao-Feng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6828693/
https://www.ncbi.nlm.nih.gov/pubmed/31685898
http://dx.doi.org/10.1038/s41598-019-52419-8
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author Wei, Yi
Zhang, Xing-Qiu
Shao, Zhu-Yan
Gao, Jian-Qiang
Yang, Xiao-Feng
author_facet Wei, Yi
Zhang, Xing-Qiu
Shao, Zhu-Yan
Gao, Jian-Qiang
Yang, Xiao-Feng
author_sort Wei, Yi
collection PubMed
description The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic scheme for the generalized KdV equation based on the Fourier pseudo-spectral method and the symplectic Euler scheme is constructed. Through a numerical examination, the explicit multi-symplectic Fourier pseudo-spectral scheme for the generalized KdV equation not only preserve the discrete global energy conservation law and the global momentum conservation law with high accuracy, but show long-time numerical stability as well.
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spelling pubmed-68286932019-11-12 Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle Wei, Yi Zhang, Xing-Qiu Shao, Zhu-Yan Gao, Jian-Qiang Yang, Xiao-Feng Sci Rep Article The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic scheme for the generalized KdV equation based on the Fourier pseudo-spectral method and the symplectic Euler scheme is constructed. Through a numerical examination, the explicit multi-symplectic Fourier pseudo-spectral scheme for the generalized KdV equation not only preserve the discrete global energy conservation law and the global momentum conservation law with high accuracy, but show long-time numerical stability as well. Nature Publishing Group UK 2019-11-04 /pmc/articles/PMC6828693/ /pubmed/31685898 http://dx.doi.org/10.1038/s41598-019-52419-8 Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Wei, Yi
Zhang, Xing-Qiu
Shao, Zhu-Yan
Gao, Jian-Qiang
Yang, Xiao-Feng
Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
title Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
title_full Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
title_fullStr Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
title_full_unstemmed Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
title_short Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle
title_sort multi-symplectic integrator of the generalized kdv-type equation based on the variational principle
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6828693/
https://www.ncbi.nlm.nih.gov/pubmed/31685898
http://dx.doi.org/10.1038/s41598-019-52419-8
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