Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves
The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provid...
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| Format: | Article |
| Language: | English |
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Shahid Chamran University of Ahvaz
2020-10-01
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| Series: | Journal of Applied and Computational Mechanics |
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| Online Access: | http://jacm.scu.ac.ir/article_14813_8b0dfa05f9a51fdccf54b6270fc5401d.pdf |
| _version_ | 1819043371843321856 |
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| author | Ji-Huan He |
| author_facet | Ji-Huan He |
| author_sort | Ji-Huan He |
| collection | DOAJ |
| description | The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of the equation. |
| first_indexed | 2024-12-21T09:55:44Z |
| format | Article |
| id | doaj.art-71613e0d6dad418d9ff73204167b439a |
| institution | Directory Open Access Journal |
| issn | 2383-4536 2383-4536 |
| language | English |
| last_indexed | 2024-12-21T09:55:44Z |
| publishDate | 2020-10-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj.art-71613e0d6dad418d9ff73204167b439a2022-12-21T19:08:04ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362020-10-016473574010.22055/jacm.2019.1481314813Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water WavesJi-Huan He0School of Science, Xi'an University of Architecture and Technology, Xi’an, China | University National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou, ChinaThe unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of the equation.http://jacm.scu.ac.ir/article_14813_8b0dfa05f9a51fdccf54b6270fc5401d.pdfcontinuum assumptiontwo scale transformfractal dimensionvariational derivative |
| spellingShingle | Ji-Huan He Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves Journal of Applied and Computational Mechanics continuum assumption two scale transform fractal dimension variational derivative |
| title | Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves |
| title_full | Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves |
| title_fullStr | Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves |
| title_full_unstemmed | Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves |
| title_short | Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves |
| title_sort | variational principle for the generalized kdv burgers equation with fractal derivatives for shallow water waves |
| topic | continuum assumption two scale transform fractal dimension variational derivative |
| url | http://jacm.scu.ac.ir/article_14813_8b0dfa05f9a51fdccf54b6270fc5401d.pdf |
| work_keys_str_mv | AT jihuanhe variationalprincipleforthegeneralizedkdvburgersequationwithfractalderivativesforshallowwaterwaves |