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 originale | English |
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pagine (da-a) | 1585-1597 |
Numero di pagine | 13 |
Rivista | Theoretical and Mathematical Physics |
Volume | 133 |
Stato di pubblicazione | Published - 2002 |
All Science Journal Classification (ASJC) codes
- ???subjectarea.asjc.3100.3109???
- ???subjectarea.asjc.2600.2610???