Geometry of spectral curves and all order dispersive integrable system

Details Geometry of spectral curves and all order dispersive integrable system Geometry of spectral curves and all order dispersive integrable system

2011-10-22

arxiv.org/abs/1110.4936v1

Physics

Mathematical Physics

69 pages, 1 figure

Scientific paper

We propose a definition for the tau function and a Baker-Akhiezer spinor kernel of an integrable system whose times parametrize slow deformations (at a speed 1/N) of a given algebraic plane curve. This definition is a full asymptotic series in 1/N involving theta functions. The large N limit of this construction reproduces the algebro-geometric solutions of the multi-KP equation. We check that our tau function satisfies Hirota equations to the first two orders, and we conjecture that they hold to all orders. The Hirota equations are equivalent to a self-replication property for the Baker-Akhiezer spinor kernel. We analyse its consequences, namely the reconstruction of a isomonodromic problem given by a Lax pair, and the relation between "correlators", the tau function and the Baker-Akhiezer spinor kernel. This construction highlights the bridges between symplectic invariants, integrable hierarchies and enumerative geometry.

Affiliated with

Also associated with

No associations

Rating

Geometry of spectral curves and all order dispersive integrable system 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 Geometry of spectral curves and all order dispersive integrable system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of spectral curves and all order dispersive integrable system will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-564246