Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains

Details Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains

2003-08-31

arxiv.org/abs/hep-th/0309010v3

Commun.Math.Phys. 259 (2005) 1-44

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, 5 figures, LaTeX; some revision of exposition, misprints corrected, the version to appear in Commun. Math. Phys

Scientific paper

10.1007/s00220-005-1387-5

We study the integrable structure of the Dirichlet boundary problem in two dimensions and extend the approach to the case of planar multiply-connected domains. The solution to the Dirichlet boundary problem in multiply-connected case is given through a quasiclassical tau-function, which generalizes the tau-function of the dispersionless Toda hierarchy. It is shown to obey an infinite hierarchy of Hirota-like equations which directly follow from properties of the Dirichlet Green function and from the Fay identities. The relation to multi-support solutions of matrix models is briefly discussed.

Affiliated with

Also associated with

No associations

Rating

Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains 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 Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-674682