Bäcklund transformations for hyperbolic surfaces in \(E^3\) via Weingarten congruences

DOI10.1007/BF02551172zbMath0965.53006MaRDI QIDQ1586689

Antoni Sym, Maciej Nieszporski

Publication date: 23 November 2000

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

\(W\)-congruencessine-Gordon equationspectral parameterBäcklund transformationsoliton theoryBianchi congruences

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05) Differential line geometry (53A25) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Cites Work

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• Geometric deformations of the evolution equations and Bäcklund transformations
• On hyperbolic surfaces: Moving triad and Loewner system connections
• Surfaces in \(\mathbb{R}^ 3\) with prescribed curvature
• Multidimensional quadrilateral lattices are integrable.
• The Darboux-Bianchi-B\"acklund transformation and soliton surfaces
• An infinite hierarchy of symmetries associated with hyperbolic surfaces
• On the characterization of Moutard transformations

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