On discrete integrable equations with convex variational principles

Details On discrete integrable equations with convex variational principles On discrete integrable equations with convex variational principles

2011-11-27

arxiv.org/abs/1111.6273v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

29 pages, 9 figures

Scientific paper

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. This gives in particular 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.

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