The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice

DOI10.1016/S0393-0440(00)00011-5zbMath0997.37052arXivsolv-int/9907012MaRDI QIDQ1589694

Adam Doliwa, Paolo Maria Santíni

Publication date: 19 November 2002

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

Full work available at URL: https://arxiv.org/abs/solv-int/9907012

zbMATH Keywords

circular latticeintegrable reductionsquadrilateral latticemultidimensional quadrilateral lattice\(d\)-invariant latticeEgorov latticeplanarity constraintsymmetric lattice

Mathematics Subject Classification ID

Related Items (20)

Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps ⋮ Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme ⋮ The B-quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ Geometric discretization of the Koenigs nets ⋮ On the classification of multidimensionally consistent 3D maps ⋮ On Negatons of the Toda Lattice ⋮ Hermite-Padé approximation and integrability ⋮ Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices ⋮ The Darboux-type transformations of integrable lattices. ⋮ The pentagon relation and incidence geometry ⋮ The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ Geometric discretization of the Bianchi system ⋮ Discrete asymptotic nets and \(W\)-congruences in Plücker line geometry ⋮ Geometry of quadrilateral nets: second Hamiltonian form ⋮ Oriented associativity equations and symmetry consistent conjugate curvilinear coordinate nets ⋮ Difference systems in bond and face variables and non-potential versions of discrete integrable systems ⋮ Quantum geometry of three-dimensional lattices ⋮ On a discretization of asymptotic nets ⋮ Explicit solutions of integrable lattices ⋮ Discrete Darboux system with self-consistent sources and its symmetric reduction

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