Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917598741921792 |
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| author | Peroni, Edoardo Wang, Jing Ping |
| author_facet | Peroni, Edoardo Wang, Jing Ping |
| contents | In this paper we study the algebraic properties of a new integrable differential-difference equation. This equation can be seen as a deformation of the modified Narita-Itoh-Bogoyavlensky equation and has the Kaup-Kupershmidt equation in its continuous limit. Using its Lax representation we explicitly construct a recursion operator for this equation and prove that it is a Nijenhuis operator. Moreover, we present the bi-Hamiltonian structures for this new equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14869 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equation Peroni, Edoardo Wang, Jing Ping Exactly Solvable and Integrable Systems In this paper we study the algebraic properties of a new integrable differential-difference equation. This equation can be seen as a deformation of the modified Narita-Itoh-Bogoyavlensky equation and has the Kaup-Kupershmidt equation in its continuous limit. Using its Lax representation we explicitly construct a recursion operator for this equation and prove that it is a Nijenhuis operator. Moreover, we present the bi-Hamiltonian structures for this new equation. |
| title | Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equation |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2306.14869 |