CONFORMAL GEOMETRY OF THE (DISCRETE) SCHWARZIAN DAVEY-STEWARTSON II HIERARCHY

B. G. KONOPELCHENKO; W. K. SCHIEF

doi:10.1017/S001708950500234X

Abstract

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The conformal geometry of the Schwarzian Davey-Stewartson II hierarchy and its discrete analogue is investigated. Connections with discrete and continuous isothermic surfaces and generalised Clifford configurations are recorded. An interpretation of the Schwarzian Davey-Stewartson II flows as integrable deformations of conformally immersed surfaces is given.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Doliwa, Adam 2007. Generalized isothermic lattices. Journal of Physics A: Mathematical and Theoretical, Vol. 40, Issue. 42, p. 12539.

Schief, W.K and Konopelchenko, B.G 2009. A novel generalization of Clifford's classical point–circle configuration. Geometric interpretation of the quaternionic discrete Schwarzian Kadomtsev–Petviashvili equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 465, Issue. 2104, p. 1291.

Bohle, C. Pedit, F. and Pinkall, U. 2009. Discrete holomorphic geometry I. Darboux transformations and spectral curves. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2009, Issue. 637,

Konopelchenko, B G 2009. Discrete integrable systems and deformations of associative algebras. Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue. 45, p. 454003.

Doliwa, Adam 2010. Desargues maps and the Hirota–Miwa equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 466, Issue. 2116, p. 1177.

Doliwa, Adam 2011. The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota–Miwa system. Physics Letters A, Vol. 375, Issue. 9, p. 1219.

Shapiro, George 2013. On discrete differential geometry in twistor space. Journal of Geometry and Physics, Vol. 68, Issue. , p. 81.

Kisil, Vladimir 2019. An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library. Proceedings of the International Geometry Center, Vol. 11, Issue. 3,

Doliwa, Adam and Kosiorek, Jarosław 2020. Asymptotic, Algebraic and Geometric Aspects of Integrable Systems. Vol. 338, Issue. , p. 1.

Article contents

CONFORMAL GEOMETRY OF THE (DISCRETE) SCHWARZIAN DAVEY-STEWARTSON II HIERARCHY

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

CONFORMAL GEOMETRY OF THE (DISCRETE) SCHWARZIAN DAVEY-STEWARTSON II HIERARCHY

Abstract

Keywords

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