The main point of this paper is to give a bi-Hamiltonian approach to the Kadomtsev-Petviashvili hierarchy of integrable nonlinear differential equations with two spatial variables (as well as Sato's generalizations of this hierarchy). Up to this time, bi-Hamiltonian structures have been displayed for various reductions of these hierarchies, namely the Gelʹfand-Dikiĭ hierarchies of integrable PDEs with one spatial variable. (Also, most finite-dimensional integrable systems have by now been cast in a bi-Hamiltonian setting.) By studying natural multi-Hamiltonian structures that arise on the direct sum of $n$ copies of the dual of a Lie algebra, and letting $n$ go to infinity appropriately, this paper demonstrates bi-Hamiltonian structures for the full Kadomtsev-Petviashvili-Sato hierarchies.

Poisson-Nijenhuis structures, truncated loop algebras and Sato's KP hierarchy.

MAGNANO, Guido;
1992-01-01

Abstract

The main point of this paper is to give a bi-Hamiltonian approach to the Kadomtsev-Petviashvili hierarchy of integrable nonlinear differential equations with two spatial variables (as well as Sato's generalizations of this hierarchy). Up to this time, bi-Hamiltonian structures have been displayed for various reductions of these hierarchies, namely the Gelʹfand-Dikiĭ hierarchies of integrable PDEs with one spatial variable. (Also, most finite-dimensional integrable systems have by now been cast in a bi-Hamiltonian setting.) By studying natural multi-Hamiltonian structures that arise on the direct sum of $n$ copies of the dual of a Lie algebra, and letting $n$ go to infinity appropriately, this paper demonstrates bi-Hamiltonian structures for the full Kadomtsev-Petviashvili-Sato hierarchies.
1992
Integrable systems and quantum groups
Pavia
March 1--2, 1990
Integrable systems and quantum groups. Edited by M. Carfora, M. Martellini and A. Marzuoli.
World Scientific Publ.
142
172
G. MAGNANO; MAGRI F
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/26407
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact