The Hamiltonian structure of discrete KP equations
| dc.creator | Kisisel, Ali Ulas Ozgur | |
| dc.date | 2001-02-22 | |
| dc.date.accessioned | 2026-07-07T04:28:19Z | |
| dc.date.available | 2026-07-07T04:28:19Z | |
| dc.description | This paper investigates Hamiltonian properties of the algebro-geometric discretization of KP hierarchy introduced in \cite{Gie1}. A Poisson bracket is introduced. The system is related to the periodic band matrix system of \cite{vM-M}. It is shown that the bracket descends to the latter and endows it with bi-Hamiltonian structure together with the first bracket already considered in \cite{vM-M}. On the other hand a bi-Hamiltonian structure for discrete KP seems to be absent for fundamental reasons. It is proven that the conserved quantities of both systems are in involution with respect to the bracket. A construction relating the bracket to a certain intersection pairing of cycles on a discrete torus is shown. This pairing is reminiscent of the intersection pairing in ``string topology'' \cite{C-S}. | |
| dc.description | 47 pages, 2 figures. Available also at http://www.math.metu.edu.tr/~akisisel | |
| dc.identifier | https://arxiv.org/abs/math-ph/0102025 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0102025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56741 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Algebra | |
| dc.title | The Hamiltonian structure of discrete KP equations | |
| dc.type | text |