Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry

DOI10.2991/jnmp.2001.8.s.16zbMath0990.37055OpenAlexW4251746047WikidataQ104434210 ScholiaQ104434210MaRDI QIDQ2732461

Adam Doliwa

Publication date: 20 January 2002

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2991/jnmp.2001.8.s.16

zbMATH Keywords

\(W\)-congruencesasymptotic netsPlücker line geometryasymptotic lattices

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Discrete version of topics in analysis (39A12) 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

Discrete Laplace cycles of period four

Cites Work

• \(\bar \partial\)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice
• Quadratic reductions of quadrilateral lattices
• The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices
• Darboux transformations for multidimensional quadrilateral lattices. I
• Multidimensional quadrilateral lattices are integrable.
• Geometric discretisation of the Toda system.
• Superposition principles associated with the Moutard transformation: an integrable discretization of a (2+1)–dimensional sine–Gordon system
• Three–dimensional integrable lattices in Euclidean spaces: conjugacy and orthogonality