Polynomial dynamical systems associated with the KdV hierarchy
In 1974, S.P. Novikov introduced the stationary n-equations of the Korteweg–de Vries hierarchy, namely the n-Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial 2n integrals, in ℂ3n. In this paper, we construct an infinite-dimensional polynomial dyna...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003140 |
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| Summary: | In 1974, S.P. Novikov introduced the stationary n-equations of the Korteweg–de Vries hierarchy, namely the n-Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial 2n integrals, in ℂ3n. In this paper, we construct an infinite-dimensional polynomial dynamical system that is universal for all dynamical systems corresponding to the n-Novikov equations. Thus, we solve the well-known problem of the relationship between the n-Novikov equations for different n. |
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| ISSN: | 2666-8181 |