2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51948We 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.Based on the talks given by the authors at NATO ARW on Hirota equations, Elba, Italy, September 2002; LaTeX, 13 pages, 3 figuresHigh Energy Physics - Theorytext