Darboux transformations for multidimensional quadrilateral lattices. I

DOI10.1016/S0375-9601(97)00341-1zbMath1006.37501MaRDI QIDQ1968358

Manuel Mañas, Paolo Maria Santíni, Adam Doliwa

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Mathematics Subject Classification ID

Related Items (28)

Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator ⋮ Discrete three-dimensional three wave interaction equation with self-consistent sources ⋮ The B-quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ Geometric discretization of the 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 ⋮ Lagrangian 3-form structure for the Darboux system and the KP hierarchy ⋮ Discrete Levy transformations and Casorati determinant solutions of quadrilateral lattices ⋮ Quadrilateral lattices and eigenfunction potentials for \(N\)-component KP hierarchies ⋮ Multidimensional quadrilateral lattices are integrable. ⋮ Extended rational expansion method for differential-difference equation ⋮ Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry ⋮ Transformations of quadrilateral lattices ⋮ Applying He's variational iteration method for solving differential-difference equation ⋮ He's homotopy perturbation method for nonlinear differential-difference equations ⋮ The focal geometry of circular and conical meshes ⋮ The Darboux-type transformations of integrable lattices. ⋮ The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ Discrete asymptotic nets and \(W\)-congruences in Plücker line geometry ⋮ Bilinear identities and discrete equations ⋮ Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations ⋮ Pfaffianization of the discrete three-dimensional three wave interaction equation ⋮ Quadratic reductions of quadrilateral lattices ⋮ Nets, lattices and multicomponent KP hierarchies ⋮ The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice ⋮ On a discretization of asymptotic nets ⋮ Elementary and binary Darboux transformations at rings ⋮ Discrete Darboux system with self-consistent sources and its symmetric reduction

Cites Work

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• Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows
• On the Moutard transformation for integrable partial differential equations
• Darboux transformations for the nonlinear Schrödinger equations
• Casorati determinant solutions for the discrete Painlevé III equation
• Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method

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