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ON THE DIRICHLET BOUNDARY PROBLEM AND HIROTA EQUATIONS

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Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete

Part of the book series: NATO Science Series ((NAII,volume 201))

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Abstract

We review the integrable structure of the Dirichlet boundary problem in two dimensions. The solution to the Dirichlet boundary problem for simplyconnected 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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Author information

Authors and Affiliations

  1. Theory Department, P.N. Lebedev Physics Institute and ITEP, Moscow, Russia

    A. Marshakov

  2. Institute of Biochemical Physics and ITEP, Moscow, Russia

    A. Zabrodin

Authors
  1. A. Marshakov
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  2. A. Zabrodin
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Editor information

Editors and Affiliations

  1. Russian Academy of Sciences, St. Petersburg, Russia

    Ludwig Faddeev

  2. Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Pierre Van Moerbeke

  3. Vrije Universiteit Brussel, Belgium

    Franklin Lambert

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Marshakov, A., Zabrodin, A. (2006). ON THE DIRICHLET BOUNDARY PROBLEM AND HIROTA EQUATIONS. In: Faddeev, L., Van Moerbeke, P., Lambert, F. (eds) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete. NATO Science Series, vol 201. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3503-6_16

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