Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity
In the present paper, an integrable semi-discretization of the modified Camassa-Holm (mCH) equation with cubic nonlinearity is presented. The key points of the construction are based on the discrete Kadomtsev-Petviashvili (KP) equation and an appropriate definition of discrete reciprocal transformat...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212604 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity. Bao-Feng Feng, Heng-Chun Hu, Han-Han Sheng, Wei Yin and Guo-Fu Yu. SIGMA 20 (2024), 091, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735647136022528 |
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| author | Feng, Bao-Feng Hu, Heng-Chun Sheng, Han-Han Yin, Wei Yu, Guo-Fu |
| author_facet | Feng, Bao-Feng Hu, Heng-Chun Sheng, Han-Han Yin, Wei Yu, Guo-Fu |
| citation_txt | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity. Bao-Feng Feng, Heng-Chun Hu, Han-Han Sheng, Wei Yin and Guo-Fu Yu. SIGMA 20 (2024), 091, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the present paper, an integrable semi-discretization of the modified Camassa-Holm (mCH) equation with cubic nonlinearity is presented. The key points of the construction are based on the discrete Kadomtsev-Petviashvili (KP) equation and an appropriate definition of discrete reciprocal transformations. First, we demonstrate that these bilinear equations and their determinant solutions can be derived from the discrete KP equation through Miwa transformation and some reductions. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solutions in the Gram-type determinant form. Finally, we obtain an integrable semi-discrete analog of the mCH equation by introducing dependent variables and a discrete reciprocal transformation. It is also shown that the semi-discrete mCH equation converges to the continuous one in the continuum limit.
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| first_indexed | 2026-03-21T18:24:32Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212604 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:24:32Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
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| spelling | Feng, Bao-Feng Hu, Heng-Chun Sheng, Han-Han Yin, Wei Yu, Guo-Fu 2026-02-09T08:05:07Z 2024 Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity. Bao-Feng Feng, Heng-Chun Hu, Han-Han Sheng, Wei Yin and Guo-Fu Yu. SIGMA 20 (2024), 091, 14 pages 1815-0659 2020 Mathematics Subject Classification: 35Q53; 37K10; 35C05; 37K40 arXiv:2404.18372 https://nasplib.isofts.kiev.ua/handle/123456789/212604 https://doi.org/10.3842/SIGMA.2024.091 In the present paper, an integrable semi-discretization of the modified Camassa-Holm (mCH) equation with cubic nonlinearity is presented. The key points of the construction are based on the discrete Kadomtsev-Petviashvili (KP) equation and an appropriate definition of discrete reciprocal transformations. First, we demonstrate that these bilinear equations and their determinant solutions can be derived from the discrete KP equation through Miwa transformation and some reductions. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solutions in the Gram-type determinant form. Finally, we obtain an integrable semi-discrete analog of the mCH equation by introducing dependent variables and a discrete reciprocal transformation. It is also shown that the semi-discrete mCH equation converges to the continuous one in the continuum limit. We greatly appreciate the anonymous referees’ useful comments, which help us improve the present paper significantly. G.-F. Yu is supported by the National Natural Science Foundation of China (Grant nos. 12175155, 12371251), Shanghai Frontier Research Institute for Modern Analysis, and the Fundamental Research Funds for the Central Universities. B.-F. Feng’s work is supported by the U.S. Department of Defense (DoD), Air Force Office of Scientific Research (AFOSR) under grant No. W911NF2010276. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity Article published earlier |
| spellingShingle | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity Feng, Bao-Feng Hu, Heng-Chun Sheng, Han-Han Yin, Wei Yu, Guo-Fu |
| title | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity |
| title_full | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity |
| title_fullStr | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity |
| title_full_unstemmed | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity |
| title_short | Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity |
| title_sort | integrable semi-discretization for a modified camassa-holm equation with cubic nonlinearity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212604 |
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