The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices
From MaRDI portal
Publication:1966428
DOI10.1016/S0375-9601(97)00657-9zbMath0969.37528WikidataQ104434220 ScholiaQ104434220MaRDI QIDQ1966428
Jan L. Cieśliński, Adam Doliwa, Paolo Maria Santíni
Publication date: 7 March 2000
Published in: Physics Letters. A (Search for Journal in Brave)
Discrete version of topics in analysis (39A12) Lattice dynamics; integrable lattice equations (37K60)
Related Items
On non-multiaffine consistent-around-the-cube lattice equations, A \(2\times 2\) Lax representation, associated family, and Bäcklund transformation for circular K-nets, The B-quadrilateral lattice, its transformations and the algebro-geometric construction, The cross ratio and Clifford algebras, On discrete differential geometry in twistor space, Integrability and geometry of the Wynn recurrence, Lagrangian 3-form structure for the Darboux system and the KP hierarchy, Curvature line parametrized surfaces and orthogonal coordinate systems: discretization with Dupin cyclides, Discretization of asymptotic line parametrizations using hyperboloid surface patches, The spectral interpretation of \(n\)-spaces of constant negative curvature immersed in \({\mathbb{R}}^{2n-1}\), Discrete Levy transformations and Casorati determinant solutions of quadrilateral lattices, Generating quadrilateral and circular lattices in KP theory, Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry, Transformations of quadrilateral lattices, Discretization of multidimensional submanifolds associated with Spin-valued spectral problems, On semidiscrete constant mean curvature surfaces and their associated families, The focal geometry of circular and conical meshes, The pentagon relation and incidence geometry, Geometric discretization of the Bianchi system, The curvature line parametrization from circular nets on a surface, Affine Spheres: Discretization via Duality Relations, Trapezoidal discrete surfaces: geometry and integrability, Discrete cyclic systems and circle congruences, Quadratic reductions of quadrilateral lattices, Nets, lattices and multicomponent KP hierarchies, Quantum geometry of three-dimensional lattices, The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice, On a discretization of asymptotic nets, Explicit solutions of integrable lattices, Discrete Darboux system with self-consistent sources and its symmetric reduction
Cites Work
- Multidimensional nonlinear integrable systems and methods for constructing their solutions
- Discrete surfaces with constant negative Gaussian curvature and the Hirota equation.
- Multidimensional quadrilateral lattices are integrable.
- Geometric discretisation of the Toda system.
- Nonlinear differential difference equations as Backlund transformations
- Integrable dynamics of a discrete curve and the Ablowitz–Ladik hierarchy
- Discrete isothermic surfaces.
- Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method
- Geometry. I, II. Transl. from the French by M. Cole and S. Levy
- Unnamed Item
