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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova

Trudy Mat. Inst. Steklova, 1999, Volume 225, Pages 21–45 (Mi tm711)

Discrete Analogs of the Darboux–Egorov Metrics
A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever

This publication is cited in the following articles:
  1. A. Sennindzher, “O diskretnykh ortogonalnykh koordinatakh, otvechayuschikh puchkam bez krucheniya nad privodimymi spektralnymi krivymi”, Sib. matem. zhurn., 65:5 (2024), 1029–774  mathnet  crossref
  2. A. E. Mironov, A. Senninger, I. A. Taimanov, “Orthogonal Curvilinear Coordinate Systems and Torsion-Free Sheaves over Reducible Spectral Curves”, Math. Notes, 114:4 (2023), 573–582  mathnet  crossref  crossref
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  4. Bobenko I A., Schief W.K., Suris Yu.B., Techter J., “On a Discretization of Confocal Quadrics. a Geometric Approach to General Parametrizations”, Int. Math. Res. Notices, 2020:24 (2020), 10180–10230  crossref  isi
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  9. B. O. Vasilevskii, “A Sufficient Nonsingularity Condition for a Discrete Finite-Gap One-Energy Two-Dimensional Schrödinger Operator on the Quad-Graph”, Funct. Anal. Appl., 49:3 (2015), 210–213  mathnet  crossref  crossref  isi  elib
  10. Konopelchenko B.G., Schief W.K., “Integrable Discretization of Hodograph-Type Systems, Hyperelliptic Integrals and Whitham Equations”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 470:2172 (2014), 20140514  crossref  mathscinet  zmath  isi  elib  scopus
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  13. Bobenko A.I., Huhnen-Venedey E., “Curvature Line Parametrized Surfaces and Orthogonal Coordinate Systems: Discretization with Dupin Cyclides”, Geod. Dedic., 159:1 (2012), 207–237  crossref  mathscinet  zmath  isi  scopus
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  15. Doliwa A., “Desargues maps and the Hirota–Miwa equation”, Proceedings of the Royal Society A–Mathematical Physical and Engineering Sciences, 466:2116 (2010), 1177–1200  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  16. Zakharov D., “A Discrete Analogue of the Dirac Operator and the Discrete Modified Novikov-Veselov Hierarchy”, Int Math Res Not, 2010, no. 18, 3463–3488  crossref  mathscinet  zmath  isi  elib  scopus
  17. Doliwa A., “The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction”, J Geom Phys, 60:5 (2010), 690–707  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  18. Doliwa A., Nieszporski M., “Darboux transformations for linear operators on two–dimensional regular lattices”, Journal of Physics A–Mathematical and Theoretical, 42:45 (2009), 454001  crossref  mathscinet  adsnasa  isi  scopus  scopus
  19. A. I. Bobenko, Yu. B. Suris, “On organizing principles of discrete differential geometry. Geometry of spheres”, Russian Math. Surveys, 62:1 (2007), 1–43  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  20. Sergeev S.M., “Quantization of three–wave equations”, Journal of Physics A–Mathematical and Theoretical, 40:42 (2007), 12709–12724  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  21. Doliwa A., Grinevich P., Nieszporski M., Santini P.M., “Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy–Riemann) 4–point equation to the self–adjoint 5–point scheme”, Journal of Mathematical Physics, 48:1 (2007), 013513  crossref  mathscinet  adsnasa  isi  scopus  scopus
  22. A. E. Mironov, I. A. Taimanov, “Orthogonal Curvilinear Coordinate Systems Corresponding to Singular Spectral Curves”, Proc. Steklov Inst. Math., 255 (2006), 169–184  mathnet  crossref  mathscinet
  23. Doliwa A., “The Normal Dual Congruences and the Dual Bianchi Lattice”, Glasg. Math. J., 47A (2005), 51–63  crossref  mathscinet  zmath  isi  elib  scopus
  24. Bobenko A.I., Matthes D., Suris Y.B., “Discrete and smooth orthogonal systems: C–infinity–approximation”, International Mathematics Research Notices, 2003, no. 45, 2415–2459  crossref  mathscinet  zmath  isi


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