420 citations · 1.3k across the 61 of their papers we have counts for
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On discrete integrable equations with convex variational principles
Alexander I. Bobenko, Felix Günther
We investigate the variational structure of discrete Laplace-type equations that are motivated by discrete integrable quad-equations. In particular, we explain why the reality cond…
Classification of integrable discrete equations of octahedron type
Vsevolod E. Adler, Alexander I. Bobenko, Yuri B. Suris
We use the consistency approach to classify discrete integrable 3D equations of the octahedron type. They are naturally treated on the root lattice and are consistent on t…
On the Lagrangian structure of integrable quad-equations
Alexander I. Bobenko, Yuri B. Suris
The new idea of flip invariance of action functionals in multidimensional lattices was recently highlighted as a key feature of discrete integrable systems. Flip invariance was pro…
Discrete nonlinear hyperbolic equations. Classification of integrable cases
Vsevolod E. Adler, Alexander I. Bobenko, Yuri B. Suris
We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on the square lattice. The fields are associated to the vertices and an equation Q(x_1,x_2,x_3,x_4…
Computing Riemann Theta Functions
Bernard Deconinck, Matthias Heil, Alexander Bobenko +2
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathemati…
Integrable non-commutative equations on quad-graphs. The consistency approach
A. I. Bobenko, Yu. B. Suris
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary a…
Classification of integrable equations on quad-graphs. The consistency approach
V. E. Adler, A. I. Bobenko, Yu. B. Suris
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basi…
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…