5 papers
Integrable systems on quad-graphs
Alexander I. Bobenko, Yuri B. Suris
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in…
Hexagonal circle patterns and integrable systems: Patterns with the multi-ratio property and Lax equations on the regular triangular lattice
A. I. Bobenko, T. Hoffmann, Yu. B. Suris
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six in…
The motion of a rigid body in a quadratic potential: an integrable discretization
Yuri B. Suris
The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We gi…
Discrete Lagrangian reduction, discrete Euler-Poincare equations, and semidirect products
Alexander I. Bobenko, Yuri B. Suris
A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on , where is a Lie group. We consider the case when the L…
Miura transformations for Toda--type integrable systems, with applications to the problem of integrable discretizations
Yuri B. Suris
We study lattice Miura transformations for the Toda and Volterra lattices, relativistic Toda and Volterra lattices, and their modifications. In particular, we give three successive…