Quadratic reductions of quadrilateral lattices

DOI10.1016/S0393-0440(98)00053-9zbMath0963.37061arXivsolv-int/9802011MaRDI QIDQ1299345

Adam Doliwa

Publication date: 23 August 1999

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

Full work available at URL: https://arxiv.org/abs/solv-int/9802011

zbMATH Keywords

integrabilitybinary Darboux transformationmultidimensional quadrilateral latticeRibaucour reduction

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Möbius geometries (51B10)

Related Items

The B-quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ Geometric discretization of the Koenigs nets ⋮ On discrete differential geometry in twistor space ⋮ The Ribaucour families of discrete R-congruences ⋮ Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry ⋮ Discrete KP equation with self-consistent sources ⋮ The Darboux-type transformations of integrable lattices. ⋮ 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 ⋮ Integrable discrete nets in Grassmannians ⋮ The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice

Cites Work

• Holomorphic curves and Toda systems
• Circle patterns with the combinatorics of the square grid
• Construction of higher-dimensional nonlinear integrable systems and of their solutions
• Discrete surfaces with constant negative Gaussian curvature and the Hirota equation.
• \(\bar \partial\)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice
• 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.
• Description of the \(n\)-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. I: Integration of the Lamé equations
• Simple waves in quasilinear hyperbolic systems. I. Theory of simple waves and simple states. Examples of applications
• Simple waves in quasilinear hyperbolic systems. II. Riemann invariants for the problem of simple wave interactions
• Method for Generating Discrete Soliton Equation. III
• Vectorial Ribaucour transformations for the Lamé equations
• Harmonic maps and periodic Toda systems
• On the unification of classical and novel integrable surfaces. I. Differential geometry
• 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item