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Geometry of Inhomogeneous Poisson Brackets, Multicomponent Harry Dym Hierarchies, and Multicomponent Hunter–Saxton Equationsстатья
Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus- Автор: Konyaev A.Y.
- Журнал: Russian Journal of Mathematical Physics
- Том: 29
- Год издания: 2022
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 518
- Последняя страница: 541
- DOI: 10.1134/S1061920822040100
- Аннотация: We introduce a natural class of multicomponent local Poisson structures P_k + P_1, where P_1 is a local Poisson bracket of order one and P_k is a homogeneous Poisson bracket of odd order k under the assumption that P_k has Darboux coordinates (Darboux–Poisson bracket) and is nondegenerate. For such brackets, we obtain general formulas in arbitrary coordinates, find normal forms (related to Frobenius triples), and provide the description of the Casimirs, using a purely algebraic procedure. In the two-component case, we completely classify such brackets up to a point transformation. From the description of Casimirs, we derive new Harry Dym (HD) hierarchies and new Hunter–Saxton (HS) equations for arbitrary number of components. In the two-component case, our HS equation differs from the well-known HS2 equation.
- Добавил в систему: Коняев Андрей Юрьевич