Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle Article Swipe
Yi Wei
,
Xingqiu Zhang
,
Zhuyan Shao
,
Jianqiang Gao
,
Xiao-Feng Yang
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1038/s41598-019-52419-8
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1038/s41598-019-52419-8
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.
Related Topics
Concepts
Symplectic geometry
Korteweg–de Vries equation
Conservation law
Mathematics
Euler's formula
Semi-implicit Euler method
Variational integrator
Applied mathematics
Mathematical analysis
Euler equations
Integrator
Physics
Backward Euler method
Quantum mechanics
Nonlinear system
Voltage
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1038/s41598-019-52419-8
- https://www.nature.com/articles/s41598-019-52419-8.pdf
- OA Status
- gold
- Cited By
- 4
- References
- 32
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2989049701
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2989049701Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1038/s41598-019-52419-8Digital Object Identifier
- Title
-
Multi-symplectic integrator of the generalized KdV-type equation based on the variational principleWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-11-04Full publication date if available
- Authors
-
Yi Wei, Xingqiu Zhang, Zhuyan Shao, Jianqiang Gao, Xiao-Feng YangList of authors in order
- Landing page
-
https://doi.org/10.1038/s41598-019-52419-8Publisher landing page
- PDF URL
-
https://www.nature.com/articles/s41598-019-52419-8.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://www.nature.com/articles/s41598-019-52419-8.pdfDirect OA link when available
- Concepts
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Symplectic geometry, Korteweg–de Vries equation, Conservation law, Mathematics, Euler's formula, Semi-implicit Euler method, Variational integrator, Applied mathematics, Mathematical analysis, Euler equations, Integrator, Physics, Backward Euler method, Quantum mechanics, Nonlinear system, VoltageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
4Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2022: 3Per-year citation counts (last 5 years)
- References (count)
-
32Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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