The Hamiltonian structure of discrete KP equations

Details The Hamiltonian structure of discrete KP equations The Hamiltonian structure of discrete KP equations

2001-02-22

arxiv.org/abs/math-ph/0102025v1

Physics

Mathematical Physics

47 pages, 2 figures. Available also at http://www.math.metu.edu.tr/~akisisel

Scientific paper

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}.

Affiliated with

Also associated with

No associations

Rating

The Hamiltonian structure of discrete KP equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Hamiltonian structure of discrete KP equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Hamiltonian structure of discrete KP equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-726591