On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917175472685056 |
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| author | Garifullin, R. N. Habibullin, I. T. |
| author_facet | Garifullin, R. N. Habibullin, I. T. |
| contents | This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations, called Toda-type chains, is that they admit finite-field reductions in the form of open chains with enhanced integrability. The paper results in a theorem stating that all known integrable Toda-type chains admit reductions in the form of an open chain of length three with a family of second-order evolutionary type symmetries. Apparently, this property of Toda-type chains can be used as an effective classification criterion when compiling lists of integrable differential-difference equations in 3D. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries Garifullin, R. N. Habibullin, I. T. Exactly Solvable and Integrable Systems This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations, called Toda-type chains, is that they admit finite-field reductions in the form of open chains with enhanced integrability. The paper results in a theorem stating that all known integrable Toda-type chains admit reductions in the form of an open chain of length three with a family of second-order evolutionary type symmetries. Apparently, this property of Toda-type chains can be used as an effective classification criterion when compiling lists of integrable differential-difference equations in 3D. |
| title | On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2512.23984 |