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Integrability of and differential–algebraic structures for spatially 1D hydrodynamical systems of Riemann typeстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 26 августа 2016 г.
- Авторы: Blackmore D., Prykarpatsky Y.A., Bogolubov N.N.Jr, Prykarpatsky A.K.
- Журнал: Chaos, Solitons and Fractals
- Том: 59
- Год издания: 2014
- Издательство: Pergamon Press Ltd.
- Местоположение издательства: United Kingdom
- Первая страница: 59
- Последняя страница: 81
- DOI: 10.1016/j.chaos.2013.11.012
- Аннотация: A differential–algebraic approach to studying the Lax integrability of a generalized Riemann type hydrodynamic hierarchy is revisited and a new Lax representation is constructed. The related bi-Hamiltonian integrability and compatible Poissonian structures of this hierarchy are also investigated using gradient-holonomic and geometric methods. The complete integrability of a new generalized Riemann hydrodynamic system is studied via a novel combination of symplectic and differential–algebraic tools. A compatible pair of polynomial Poissonian structures, a Lax representation and a related infinite hierarchy of conservation laws are obtained. In addition, the differential–algebraic approach is used to prove the complete Lax integrability of the generalized Ostrovsky–Vakhnenko and a new Burgers type system, and special cases are studied using symplectic and gradient-holonomic tools. Compatible pairs of polynomial Poissonian structures, matrix Lax representations and infinite hierarchies of conservation laws are derived.
- Добавил в систему: Боголюбов Николай Николаевич