# Integrable systems on quad-graphs

@article{Bobenko2001IntegrableSO, title={Integrable systems on quad-graphs}, author={Alexander I. Bobenko and Yuri B. Suris}, journal={International Mathematics Research Notices}, year={2001}, volume={2002}, pages={573-611} }

Discrete (lattice) systems constitute a well-established part of the theory of integrable systems. They came up already in the early days of the theory (see, e.g. [11, 12]), and took gradually more and more important place in it (cf. a review in [18]). Nowadays many experts in the field agree that discrete integrable systems are in many respects even more fundamental than the continuous ones. They play a prominent role in various applications of integrable systems such as discrete differential…

## 286 Citations

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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 basis of the…

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- 2003

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- MathematicsInternational Mathematics Research Notices
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