Discrete asymptotic nets and \(W\)-congruences in Plücker line geometry

DOI10.1016/S0393-0440(00)00070-XzbMath0990.37056arXivsolv-int/9909015WikidataQ104434212 ScholiaQ104434212MaRDI QIDQ5943192

Adam Doliwa

Publication date: 20 January 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9909015

zbMATH Keywords

\(W\)-congruencesintegrability of asymptotic latticesquadrilateral lattices

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05)

Related Items

Geometric discretization of the Koenigs nets ⋮ On discrete differential geometry in twistor space ⋮ Discrete Laplace cycles of period four ⋮ Discretization of asymptotic line parametrizations using hyperboloid surface patches ⋮ Gaussian and mean curvatures for discrete asymptotic nets ⋮ Nonlinear hyperbolic equations in surface theory: Integrable discretizations and approximation results ⋮ Integrable discrete nets in Grassmannians ⋮ On a discretization of asymptotic nets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrete surfaces with constant negative Gaussian curvature and the Hirota equation.
• Quadratic reductions of quadrilateral lattices
• Quantum integrable models and discrete classical Hirota equations
• The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice
• On a discretization of asymptotic nets
• Self-dual Einstein spaces via a permutability theorem for the Tzitzeica equation.
• Darboux transformations for multidimensional quadrilateral lattices. I
• Multidimensional quadrilateral lattices are integrable.
• Geometric discretisation of the Toda system.
• Projective generalizations of Lelieuvre's formula
• Transformations of quadrilateral lattices
• Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation
• Superposition principles associated with the Moutard transformation: an integrable discretization of a (2+1)–dimensional sine–Gordon system
• Bäcklund transformations and nonlinear differential difference equations
• Charged free fermions, vertex operators and the classical theory of conjugate nets
• Three–dimensional integrable lattices in Euclidean spaces: conjugacy and orthogonality
• An algebraic formula for superposition and the completeness of the Bäcklund transformations of (2+1)-dimensional integrable systems
• Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method