The bi-Hamiltonian theory of the Harry Dym equation

M. Pedroni, V. Sciacca, J. P. Zubelli

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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.

Original languageBritish English
Pages (from-to)1585-1597
Number of pages13
JournalTheoretical and Mathematical Physics(Russian Federation)
Volume133
Issue number2
DOIs
StatePublished - 2002

Keywords

  • Bi-Hamiltonian formalism
  • Completely integrable systems
  • Harry Dym equation

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