420 citations · 1.3k across the 61 of their papers we have counts for
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Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results
A. I. Bobenko, D. Matthes, Yu. B. Suris
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence resul…
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…
Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions
Alexander I. Bobenko, Tatyana V. Pavlyukevich, Boris A. Springborn
We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modific…
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…
Variational principles for circle patterns and Koebe's theorem
Alexander I. Bobenko, Boris A. Springborn
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--on…
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…