The Modified Toda Hierarchy
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910738667274240 |
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| author | Rui, Wenjuan Guan, Wenchuang Yang, Yi Cheng, Jipeng |
| author_facet | Rui, Wenjuan Guan, Wenchuang Yang, Yi Cheng, Jipeng |
| contents | In this paper, modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called mToda hierarchy. Inspired by the fact that Toda hierarchy is 2-component generalization of usual KP hierarchy, mToda hierarchy is constructed from bilinear equations of 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 Toda and mToda hierarchies, which means the definition of mToda hierarchy here is reasonable. Finally, Darboux transformations of the Toda and mToda hierarchies are also constructed by using the aforementioned Miura links. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_09450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Modified Toda Hierarchy Rui, Wenjuan Guan, Wenchuang Yang, Yi Cheng, Jipeng Exactly Solvable and Integrable Systems Mathematical Physics 35Q51, 37K10, 37K40 In this paper, modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called mToda hierarchy. Inspired by the fact that Toda hierarchy is 2-component generalization of usual KP hierarchy, mToda hierarchy is constructed from bilinear equations of 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 Toda and mToda hierarchies, which means the definition of mToda hierarchy here is reasonable. Finally, Darboux transformations of the Toda and mToda hierarchies are also constructed by using the aforementioned Miura links. |
| title | The Modified Toda Hierarchy |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 35Q51, 37K10, 37K40 |
| url | https://arxiv.org/abs/2408.09450 |