The bi-Hamiltonian theory of the Harry Dym equation

Vincenzo Sciacca, Zubelli, Pedroni

Risultato della ricerca: Article

6 Citazioni (Scopus)

Abstract

We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved using a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev-Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such a system the HD-KP hierarchy. We then construct an infinite system of ordinary differential equations (in infinitely many variables) that is equivalent to the HD-KP hierarchy. Its role is analogous to the role of the Central System in the Kadomtsev-Petviashivili hierarchy.
Lingua originaleEnglish
pagine (da-a)1585-1597
Numero di pagine13
RivistaTheoretical and Mathematical Physics
Volume133
Stato di pubblicazionePublished - 2002

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hierarchies
KP Hierarchy
Hamiltonian Formalism
Soliton Equation
Poisson Structure
Infinite Systems
Korteweg-de Vries Equation
System of Ordinary Differential Equations
Siméon Denis Poisson
Analogue
differential equations
solitary waves
Hierarchy
analogs
formalism

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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The bi-Hamiltonian theory of the Harry Dym equation. / Sciacca, Vincenzo; Zubelli; Pedroni.

In: Theoretical and Mathematical Physics, Vol. 133, 2002, pag. 1585-1597.

Risultato della ricerca: Article

Sciacca, V, Zubelli & Pedroni 2002, 'The bi-Hamiltonian theory of the Harry Dym equation', Theoretical and Mathematical Physics, vol. 133, pagg. 1585-1597.
Sciacca V, Zubelli, Pedroni. The bi-Hamiltonian theory of the Harry Dym equation. Theoretical and Mathematical Physics. 2002;133:1585-1597.
Sciacca, Vincenzo ; Zubelli ; Pedroni. / The bi-Hamiltonian theory of the Harry Dym equation. In: Theoretical and Mathematical Physics. 2002 ; Vol. 133. pagg. 1585-1597.
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