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Letters in Mathematical Physics

, Volume 102, Issue 2, pp 181–202 | Cite as

On Discrete Integrable Equations with Convex Variational Principles

  • Alexander I. Bobenko
  • Felix Günther
Article

Abstract

The Lagrangian structure of two-dimensional integrable systems on quad-graphs is investigated. We give reality conditions under which the action functionals are strictly convex. In particular, this gives uniqueness of solutions of Dirichlet boundary value problems. In some cases, we discuss also the existence of solutions. The integrability of combinatorial data is studied. In addition, a connection between (Q3) and circle patterns is discussed.

Mathematics Subject Classification (2010)

37J35 52C26 70S05 

Keywords

discrete integrable systems integrable quad-equations Lagrangian formalism variational principle Dirichlet boundary value problem circle patterns 

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Copyright information

© Springer 2012

Authors and Affiliations

  1. 1.Institut für Mathematik, MA 8-3Technische Universität BerlinBerlinGermany

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