6533b85afe1ef96bd12b91bf
RESEARCH PRODUCT
The bi-Hamiltonian theory of the Harry Dym equation
M. PedroniJ. ZubelliVincenzo Sciaccasubject
Physics and Astronomy (all)Completely integrable systemBi-Hamiltonian formalismHarry Dym equationMathematical PhysicStatistical and Nonlinear Physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-01-01 |