### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 1585-1597 |

Numero di pagine | 13 |

Rivista | Theoretical and Mathematical Physics |

Volume | 133 |

Stato di pubblicazione | Published - 2002 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cita questo

*Theoretical and Mathematical Physics*,

*133*, 1585-1597.

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

Risultato della ricerca: Article

*Theoretical and Mathematical Physics*, vol. 133, pagg. 1585-1597.

}

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 -