Integrable Systems and Discrete Geometry

Encyclopedia of Mathematical Physics: Five-Volume Set

Volumn , Issue , 2004, Pages 78-87

  Doliwa, A ^a   Santini, P M ^b  

^a UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN   (Poland)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE GEOMETRY; INTEGRABLE SYSTEMS; SYSTEM GEOMETRY;

EID: 85070016006     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B0-12-512666-2/00178-4     Document Type: Chapter

References (18)

1. Akhmetshin AA, Krichever IM, Volvovski YS Discrete analogs of the Darboux-Egoroffmetrics. Proceedings of the Steklov Institute of Mathematics 1999, 225:16-39.
2. Białecki M, Doliwa A Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve. Communications in Mathematical Physics 2005, 253:157-170.
3. Bobenko AI Discrete differential geometry. Integrability as consistency. Discrete Integrable Systems 2004, 85-110. Springer, Berlin. B. Grammaticos, Y. Kosmann-Schwarzbach, T. Tamizhmani (Eds.).
4. Discrete Integrable Geometry and Physics 1999, Clarendon, Oxford. A.I. Bobenko, R. Seiler (Eds.).
5. Bogdanov LV, Konopelchenko BG Lattice and q-difference Darboux-Zakharov-Manakov systems via δ method. Journal of Physics A 1995, 28:L173-L178.
6. 2N-1. Physics Letters A 1997, 236:425-430.
7. Doliwa A, Grinevich PG, Nieszporski M, and Santini PM (2004) Integrable lattices and their sublattices: from the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme, nlin. SI/0410046.
8. Doliwa A, Mañas M, Martínez Alonso L, Medina E, Santini PM Charged free fermions, vertex operators and transformation theory of conjugate nets. Journal of Physics A 1999, 32:1197-1216.
9. Doliwa A, Nieszporski M, Santini PM Asymptotic lattices and their integrable reductions. I. The Bianchi and the Fubini-Ragazzi lattices. Journal of Physics A 2001, 34:10423-10439.
10. Doliwa A, Nieszporski M, Santini PM Geometric discretization of the Bianchi system. Journal of Geometry and Physics 2004, 52:217-240.
11. Doliwa A, Santini PM The symmetric, D-invariant and Egorov reductions of the quadrilateral latice. Journal of Geometry and Physics 2000, 36:60-102.
12. Doliwa A, Santini PM, Mañas M Transformations of quadrilateral lattices. Journal of Mathematical Physics 2000, 41:944-990.
13. Klimczewski P, Nieszporski M, Sym A Luigi Bianchi, Pasquale Calapso and solitons. Rend. Sem. Mat. Messina, Atti del Congresso Internazionale in Onore di Pasquale Calapso 2000, 223-240. Messina, 12-14 October 1998,.
14. Mañas M Fundamental transformation for quadrilateral lattices: first potentials and τ-functions, symmetric and pseudo-Egorov reductions. Journal of Physics A 2001, 34:10413-10421.
15. Matsuura N, Urakawa H Discrete improper affine spheres. Journal of Geometry and Physics 2003, 45:164-183.
16. Rogers C, Schief WK Bäcklund and Darboux Transformations. Geometry and Modern Applications in Soliton Theory 2002, Cambridge University Press, Cambridge.
17. Schief WK Lattice geometry of the discrete Darboux, KP, BKP and CKP equations. Menelaus' and Carnot's theorems. Journal of Nonlinear Mathematical Physics 2003, 10(suppl. 2):194-208.
18. Schief WK On the unification of classical and novel integrable surfaces. II. Difference geometry. Proceedings of the Royal Society of London A 2003, 459:373-391.