The Modified Toda Hierarchy
In this paper, the modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called the mToda hierarchy. Inspired by the fact that the Toda hierarchy is a 2-component generalization of the usual KP hierarchy, the mToda hierarchy...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212782 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Modified Toda Hierarchy. Wenjuan Rui, Wenchuang Guan, Yi Yang and Jipeng Cheng. SIGMA 20 (2024), 110, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862742430121459712 |
|---|---|
| author | Rui, Wenjuan Guan, Wenchuang Yang, Yi Cheng, Jipeng |
| author_facet | Rui, Wenjuan Guan, Wenchuang Yang, Yi Cheng, Jipeng |
| citation_txt | The Modified Toda Hierarchy. Wenjuan Rui, Wenchuang Guan, Yi Yang and Jipeng Cheng. SIGMA 20 (2024), 110, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, the modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called the mToda hierarchy. Inspired by the fact that the Toda hierarchy is a 2-component generalization of the usual KP hierarchy, the mToda hierarchy is constructed from bilinear equations of the 2-component first modified KP hierarchy, where we provide the corresponding equivalence with Lax formulations. Then it is demonstrated that there are Miura links between the Toda and mToda hierarchies, which means the definition of the mToda hierarchy here is reasonable. Finally, Darboux transformations of the Toda and mToda hierarchies are also constructed by using the aforementioned Miura links.
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| first_indexed | 2026-03-21T18:28:59Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212782 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:28:59Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rui, Wenjuan Guan, Wenchuang Yang, Yi Cheng, Jipeng 2026-02-11T10:37:48Z 2024 The Modified Toda Hierarchy. Wenjuan Rui, Wenchuang Guan, Yi Yang and Jipeng Cheng. SIGMA 20 (2024), 110, 21 pages 1815-0659 2020 Mathematics Subject Classification: 35Q51; 37K10; 37K40 arXiv:2408.09450 https://nasplib.isofts.kiev.ua/handle/123456789/212782 https://doi.org/10.3842/SIGMA.2024.110 In this paper, the modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called the mToda hierarchy. Inspired by the fact that the Toda hierarchy is a 2-component generalization of the usual KP hierarchy, the mToda hierarchy is constructed from bilinear equations of the 2-component first modified KP hierarchy, where we provide the corresponding equivalence with Lax formulations. Then it is demonstrated that there are Miura links between the Toda and mToda hierarchies, which means the definition of the mToda hierarchy here is reasonable. Finally, Darboux transformations of the Toda and mToda hierarchies are also constructed by using the aforementioned Miura links. Many thanks to the anonymous referees for their useful comments and suggestions. This work is supported by the National Natural Science Foundations of China (Nos. 12171472 and 12261072) and the “Qinglan Project” of Jiangsu University. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Modified Toda Hierarchy Article published earlier |
| spellingShingle | The Modified Toda Hierarchy Rui, Wenjuan Guan, Wenchuang Yang, Yi Cheng, Jipeng |
| title | The Modified Toda Hierarchy |
| title_full | The Modified Toda Hierarchy |
| title_fullStr | The Modified Toda Hierarchy |
| title_full_unstemmed | The Modified Toda Hierarchy |
| title_short | The Modified Toda Hierarchy |
| title_sort | modified toda hierarchy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212782 |
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