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Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
Інший ID:
2000 Mathematics Subject Classification: 37K10
Посилання:
Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy / A.K. Svinin // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ.
Підтримка:
The author thanks the organizers of Sixth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 20–26, 2005, Kyiv) for hospitality and their work which allows to create friendly atmosphere during this Conference. The present paper is the written version of the talk delivered by the author at this conference.
Дата:
2006
Переглядів:
467
Завантажень:
251
Анотація:
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these parameters. It is written down discrete equations which naturally generalize the first discrete Painlevé equation dPI in a sense that autonomous version of these equations admit the limit to the first Painlevé equation. It is shown that each of these equations describes Bäcklund transformations of Veselov-Shabat periodic dressing lattices with odd period known also as Noumi-Yamada systems of type A2(n-1)⁽¹⁾.
