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- Title
On Discrete Integrable Equations with Convex Variational Principles.
- Authors
Bobenko, Alexander; Günther, Felix
- 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.
- Subjects
DISCRETE systems; INTEGRABLE functions; VARIATIONAL principles; COMBINATORICS; EXISTENCE theorems; DIRICHLET problem; UNIQUENESS (Mathematics)
- Publication
Letters in Mathematical Physics, 2012, Vol 102, Issue 2, p181
- ISSN
0377-9017
- Publication type
Article
- DOI
10.1007/s11005-012-0583-4