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

Fingerprint

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

Cita questo

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

@article{354cf4b5cd94475bb9556ae6832d7015,
title = "The bi-Hamiltonian theory of the Harry Dym equation",
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.",
author = "Vincenzo Sciacca and Zubelli and Pedroni",
year = "2002",
language = "English",
volume = "133",
pages = "1585--1597",
journal = "Theoretical and Mathematical Physics(Russian Federation)",
issn = "0040-5779",
publisher = "Springer New York",

}

TY - JOUR

T1 - The bi-Hamiltonian theory of the Harry Dym equation

AU - Sciacca, Vincenzo

AU - Zubelli, null

AU - Pedroni, null

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/107229

M3 - Article

VL - 133

SP - 1585

EP - 1597

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

ER -