Abstract

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 $A_1$, $A_2$, where $A_1$ is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field $tau$ such that $A_2=L_tau A_1$. We use this result in order to find the Lagrangian representation when $A_2$ 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.

Autore Pugliese

• Vitolo Raffaele

Tutti gli autori

• Pavlov M.V. , Vitolo R.F.

Titolo volume/Rivista

JOURNAL OF GEOMETRY AND PHYSICS

Anno di pubblicazione

2017

ISSN

0393-0440

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

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Numero di citazioni Scopus

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Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

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