Remarks on the Lagrangian representation of bi-Hamiltonian equations

M. V. Pavlov; R. F. Vitolo

doi:10.1016/j.geomphys.2016.10.013

Remarks on the Lagrangian representation of bi-Hamiltonian equations

M. V. Pavlov, R. F. Vitolo

Лаборатория нелинейных процессов в гидродинамических системах ММФ

Результат исследования: Научные публикации в периодических изданиях › статья

2 Цитирования (Scopus)

Аннотация

The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A₁, A₂, where A₁ is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A₂=L_τA₁. We use this result in order to find the Lagrangian representation when A₂ is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.

Язык оригинала	английский
Страницы (с-по)	239-249
Число страниц	11
Журнал	Journal of Geometry and Physics
Том	113
DOI	https://doi.org/10.1016/j.geomphys.2016.10.013
Состояние	Опубликовано - 1 мар 2017

Доступ к документу

10.1016/j.geomphys.2016.10.013

Link to publication in Scopus

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Pavlov, M. V., & Vitolo, R. F. (2017). Remarks on the Lagrangian representation of bi-Hamiltonian equations. Journal of Geometry and Physics, 113, 239-249. https://doi.org/10.1016/j.geomphys.2016.10.013

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