On the Dirichlet Boundary Problem and Hirota Equations
High Energy Physics - Theory
2007-05-23 v1
Abstract
We review the integrable structure of the Dirichlet boundary problem in two dimensions. The solution to the Dirichlet boundary problem for simply-connected case is given through a quasiclassical tau-function, which satisfies the Hirota equations of the dispersionless Toda hierarchy, following from properties of the Dirichlet Green function. We also outline a possible generalization to the case of multiply-connected domains related to the multi-support solutions of matrix models.
Cite
@article{arxiv.hep-th/0305259,
title = {On the Dirichlet Boundary Problem and Hirota Equations},
author = {A. Marshakov and A. Zabrodin},
journal= {arXiv preprint arXiv:hep-th/0305259},
year = {2007}
}
Comments
Based on the talks given by the authors at NATO ARW on Hirota equations, Elba, Italy, September 2002; LaTeX, 13 pages, 3 figures