Transformations of quadrilateral lattices

DOI10.1063/1.533175zbMath0987.37070arXivsolv-int/9712017OpenAlexW3102384898WikidataQ104434214 ScholiaQ104434214MaRDI QIDQ2737862

Adam Doliwa, Manuel Mañas, Paolo Maria Santíni

Publication date: 30 August 2001

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

Full work available at URL: https://arxiv.org/abs/solv-int/9712017

zbMATH Keywords

discretizations of congruencesdiscretizations of conjugate nets

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

Multivariate orthogonal Laurent polynomials and integrable systems, Multivariate Toda hierarchies and biorthogonal polynomials, Multivariate orthogonal polynomials and integrable systems, Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator, Infinitesimal Darboux transformation and semi-discrete MKDV equation, The B-quadrilateral lattice, its transformations and the algebro-geometric construction, Geometric discretization of the Koenigs nets, Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations, On discrete differential geometry in twistor space, Discrete Ω$\Omega$‐nets and Guichard nets via discrete Koenigs nets, Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations, Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials, Hermite-Padé approximation and integrability, Discrete Laplace cycles of period four, The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system, Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices, The Ribaucour families of discrete R-congruences, Discretization of multidimensional submanifolds associated with Spin-valued spectral problems, The focal geometry of circular and conical meshes, Discrete KP equation with self-consistent sources, 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, Discrete time Toda systems, TRANSFORMATIONS OF A SPACE CURVE AND APPLICATIONS TO ELASTIC CURVES, Discrete minimal nets with symmetries, Vertex Normals and Face Curvatures of Triangle Meshes, Integrable discrete nets in Grassmannians, Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations, 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

• Construction of higher-dimensional nonlinear integrable systems and of their solutions
• \(\bar \partial\)-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
• Superposition principles associated with the Moutard transformation: an integrable discretization of a (2+1)–dimensional sine–Gordon system
• On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
• The non-local delta problem and (2+1)-dimensional soliton equations
• Bäcklund transformations and nonlinear differential difference equations
• Laplace transformations of hydrodynamic-type systems in Riemann invariants: Periodic sequences
• 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
• Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
• Generalized integrable hierarchies and Combescure symmetry transformations
• Integrable dynamics of a discrete curve and the Ablowitz–Ladik hierarchy
• Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method