On the Dirichlet Boundary Problem and Hirota Equations

Details On the Dirichlet Boundary Problem and Hirota Equations On the Dirichlet Boundary Problem and Hirota Equations

2003-05-30

arxiv.org/abs/hep-th/0305259v1

Physics

High Energy Physics

High Energy Physics - Theory

Based on the talks given by the authors at NATO ARW on Hirota equations, Elba, Italy, September 2002; LaTeX, 13 pages, 3 figur

Scientific paper

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.

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