# Remarks on the Lagrangian representation of bi-Hamiltonian equations

M. V. Pavlov, R. F. Vitolo

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

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=LτA1. 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 239-249 11 Journal of Geometry and Physics 113 https://doi.org/10.1016/j.geomphys.2016.10.013 Опубликовано - 1 мар 2017

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