Asymptotic lattices and their integrable reductions I: the Bianchi and the Fubini-Ragazzi lattices

Details Asymptotic lattices and their integrable reductions I: the Bianchi and the Fubini-Ragazzi lattices Asymptotic lattices and their integrable reductions I: the Bianchi and the Fubini-Ragazzi lattices

2001-04-30

arxiv.org/abs/nlin/0104070v1

J. Phys. A: Math. Gen. 34 (2001) 10423-10439

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, 2 figures, uses iopart style

Scientific paper

10.1088/0305-4470/34/48/308

We review recent results on asymptotic lattices and their integrable reductions. We present the theory of general asymptotic lattices in R^3 together with the corresponding theory of their Darboux-type transformations. Then we study the discrete analogues of the Bianchi surfaces and their transformations. Finally, we present the corresponding theory of the discrete analogues of the isothermally-asymptotic (Fubuni-Ragazzi) nets.

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